I have a few alternatives, with different pros and cons. I have extensive first-hand experience with each of these products.
First, a little history. SteelSeries launched the "H Wireless" headset a couple years ago. It's a wireless headset with a basestation, with a replaceable battery (two of them, in fact, with a charger in the base station), flexible boom mic, and many options for connectivity. It's over-ear, relatively comfortable, but weighs a ton. It depends on being within ~100m of the base station (it's a Class 1 2.4 GHz device) to get wireless functionality, though. You can still use it as normal headphones with a 3.5mm cable.
The Siberia 800 is basically the H Wireless, rebranded and with slight tweaks to the aesthetic.
The Siberia 840 is basically the Siberia 800, but with Bluetooth added as another option in addition to the standard wired connections (USB, 3.5mm and toslink). I emailed SteelSeries to get more details about exactly how their Bluetooth works (is it in the base station or the headset, for one), and will update you when I hear back. I'm betting the Bluetooth transceiver is in the base station, and lets you do things like stream music or calls from your phone to your base station to your headset.
My experience is solely with the H Wireless, but this product family is so incredibly similar to the original H Wireless that I basically have experience with the 840, minus the optional Bluetooth stuff.
Pros:
Two batteries - as long as you keep one charging, you'll never run out of juice. It takes about 5-10 seconds for an experienced user to swap batteries.
Sound quality - they seem to use an extremely low latency, lossless codec that's perfectly suitable for real-time gaming. Also, the sound never once dropped out or had any digital artifacts while I was using the H Wireless.
Over-ear and very large - the only possible issue you might have is that the headset feels a little heavy, and may press on your skull with an uncomfortable amount of force. Not sure if they've improved that at all with the new models. But it will definitely encompass your entire ear within the padded cup.
No special software is required to use them -- the 3.5mm / toslink / USB sound card options are all pretty standard. I think the Siberia 840 has some support for an EQ or something through SteelSeries' custom software, if you want. Meh.
Cons:
Battery life: Either the battery "fuel gauge" on the base station is wildly inaccurate, or the battery life on these Li-Ion cells deteriorates at a frightening pace with use. It was nice (around 18-20 hours) when first using the headset, but within 3-6 months it was around half that. I generally ran the batteries down to about 25% before recharging them but I never let them drain completely, so when I first got 'em, I was changing battery about once per day, and within 6 months I was changing battery about two to three times for a full day gaming session.
SteelSeries refused to sell replacement batteries for the H Wireless. Not sure if that has changed for the Siberia 800 / 840.
These cans are a bit pricier than Bob's suggestion (but, thankfully, not quite into the $400-500 price range).
Pending the result of my email to SteelSeries, even the 840 might be functionally useless as a wireless headset if you carry it away from the base station. Unless the Bluetooth codec is inside the headset itself, which would be awesome, as these could then double as Bluetooth headphones for music listening and taking calls while on travel (with a smartphone or laptop).
The next suggestion is for Bluetooth headphones with which I have extensive experience (yes, even for gaming) and represents my current personal setup.
Foreword: Whenever you're using Bluetooth in a gaming setup, it is important that both your transmitter and the headphones support AptX Low Latency. Just AptX will not be good enough. The reason is that AptX Low Latency is the only Bluetooth A2DP codec with a low enough latency to be suitable for gaming. Other codecs like AAC and "regular" AptX will sound nice, but the latency is too high for real-time gaming. You will notice the latency with any other codec, and it will drive you insane!
These headphones are truly as wonderful to wear as the marketing says they are. The marketing is stunningly honest in the way that all of their claims have been very well substantiated by my personal experience with the headphones since May 2016 (over 3 months of daily use as of this writing).
However, there is no implementation of Bluetooth on the market that provides simultaneous, high-quality audio playback and microphone capture. The standard Bluetooth profiles simply do not have anything that would make this possible. The Hands Free Profile (HFP) provides for very low-quality duplex audio, and the A2DP profile provides for very high-quality playback only.
So, in order to build a perfect gaming setup that works with Bluetooth headphones, you're going to need to let go of the requirement to make use of the mic built into the headset, and use a mic on your desk. Some people simply won't be able to accept this, but I find it works extremely well for me.
Also, since I am not aware of any Bluetooth dongles for Windows that support AptX Low Latency (this codec would have to be added to the software Bluetooth stack on Windows), you will have to buy a separate "full stack" Bluetooth transceiver for this setup. Personally I use the Imperial BART 1, but the HomeSpot will work too (make sure to get the model that says AptX Low Latency; there are several different models of device under the same product page on Amazon).
Lastly, for a mic, I just use the Blue Yeti (with a third-party pop filter). The mic is more than sufficient for voice; it's actually suitable for recording indie-grade music (singing and instruments).
Now, on to the pros and cons of the actual BeoPlay H8 headset, keeping in mind my setup above...
Pros:
Quite good battery life, and it seems to be holding up well over time, at least after 3 months.
Never any dropouts with the Imperial BART 1 or the Homespot. They do drop out with Android phones, but that's a bug in Android I believe.
Truly awesome head feel, very lightweight, and feels extremely sturdy. The cups are on-ear, but the lightness of the headset prevents fatigue pain on the ears. The cups are among the most comfortable I've ever tried on.
Perfect, artifact-free active noise cancellation (SO great for immersion!). The passive noise cancellation is also fantastic.
Sound quality with AptX Low Latency is basically equivalent to a high-end wired setup, as far as I can hear. It's a combination of the high quality acoustics, the perfect ANC, the drivers, the (lack of) a biased EQ in the DSP (it's very flat) and the high bitrate and very good lossy compression of AptX Low Latency (I understand that it's comparable to at least MP3, possibly with compression ratios approaching AAC, and they use a very generous bitrate with Bluetooth 4.0 or later).
The touch controls seem weird at first, but you'll get used to them. Presents a nice, clean human interface without any buttons (except the on/off switch).
User-replaceable battery. BeoPlay sells replacement batteries for $50. These should last you a long time.
Bluetooth 4.2 -- supports the latest Bluetooth standard, which is good for reliability and range, because they've made some iterative improvements in 4.1 and 4.2 to minimize interference with other 2.4 GHz protocols and even 4G LTE.
Dual-purpose: you can stow these in a bag or around your neck and take them on the go with a smartphone, and they're great for making phone calls or listening to music. If you have a smartphone supporting AptX Low Latency (some do), they're even suitable for smartphone/tablet real-time gaming. No voice chat at the same time, though.
Cons:
Bluetooth limitation: no simultaneous A2DP and mic capture :( But this is not specific to this headset. Until the Bluetooth standards body introduces a proper duplex profile, we're stuck with this limitation.
Cost. They're definitely a luxury item, and a proper gaming setup requires the purchase of a mic and a Bluetooth AptX LL transceiver, which drives up the cost into the $600+ range ($500 + at least $50 for a decent mic + $50ish for a transceiver).
These headphones do have some sound reliability problems after a fairly small range gap between the transceiver and your headphones. I think the BT transceiver in the headset may be Class 2 (10 meters). I can walk into the next room, but sometimes if I try to go out into the hallway and there's a wall or two between me and the transceiver, it'll start to drop out. This is with distances that never caused any sound disruption with the SteelSeries H Wireless, so there are definitely wireless solutions that have longer range than the BeoPlay H8 (this could be a Bluetooth limitation, or it might be particular to these cans, not sure). However, if you have a direct line of sight to the transmitter, you shouldn't have any problems all the way out to 10 meters -- it's only when I put a wall or door between me and the BART 1 that I have any reliability problems.
Conclusion
I basically hate the physical construction of most wireless "gaming" headsets because they think it's cool to use some weird triangular or polygonal shape that doesn't fit my ears at all and leaves huge gaps for air to get in and reduces immersion. They also generally lack ANC, are too heavy, and don't really have audiophile-grade sound production.
Though I can recommend the Siberia 800/840 if you can get over some of these limitations, the real "audiophile gamer" setup in my mind is with the BeoPlay H8. It's just pretty expensive.
Oh, and I don't do wired stuff anymore. I refuse to be wired down. It's great to walk into the next room or go to the bathroom and never miss a beat (especially if you're listening to something live, like a Teamspeak room or a baseball game, and don't want to miss anything).
