It depends mainly on the type of NAND the SSD uses, and also somewhat on the controller.
Higher quality SLC NAND stores one bit per cell. This make the cells much faster and longer lived, whereas MLC and TLC (2 bits and 3 bits) degrade more easily and are harder to read and write, especially write. Since the MLC SSDs are more common, most SSDs do have slow writes (compared to their reads)
If you just run out and get the cheapest SSD, you're likely to find yourself something faster than a HDD by only the slightest margins in read speed, like the Kingston SSDVNow. In some circumstances, this SSD will be slower than a HDD.
Larger SSDs are also faster, because they're composed of multiple chips effectively in RAID 0RAID 0 (it's similar).
OCZ Vertex, Sandisk Extreme and Samsung Pro are all models to look for if you want the fastest performance.
Alternatively, if you're on a budget (who isn't), the Samsung EVO, OCZ ARC (they've renamed their mid range a few times, but I'm pretty sure this is the newest), and the Crucial MX range are easier on the wallet.
Be sure to find some benchmarks before you buy, and remember that the newest isn't always the best. The older SSDs on larger processes are often longer lived, if you're making lots of writes. Also check out the newer SSDs with 3D V-NAND if you're concerned.