I just want to be able to play all my expansions I have about 5 expansions and on my current set up I can only play 2 expansions without horrible lag times.
The recommendation could be better if you include the specifications of the computer that has the lags in your question, so we can analyze where the bottleneck in your current setup is and if the newer hardware would be a substantial improvement.
That being said, The Sims 3 was released in 2009, is based on DirectX 9 and has moderate hardware requirements. A fairly obvious case one might say?
Core i3-4170 vs. Core i5-6400 GPU
For comparison of Intel GPUs there is a separate article in Wikipedia that gives a really useful overview, combined with the data in the lists for all the Intel processors (list-type Wikipedia links are/were banned on some SE sites, but they are not hard to find) we get this:
Core i3-4170 GPU runs at 350–1150 MHz, TDP 54 W
HD Graphics 4200, 4400, 4600, P4600, P4700 – GT2, 20 execution units, up to 432 GFLOPS at 1350 MHz
Core i5-6400 GPU runs at 350–950 MHz, TDP 65 W
HD Graphics 530, GT2 – 24 execution units, up to 441.6 GFLOPS at 1.15 GHz
For comparison, the GPU of the Ivy Brigde CPU I have in my T530:
HD Graphics 4000 – 16 execution units and additional features, up to 332.8 GFLOPS at 1300 MHz
So just by looking at the GFLOPS, there isn't really any difference between both models but about 30% increase over the older generation.
DirectX 9 in 2015 how hard could it be?
Just for a test I ran Tomb Raider (2013, DirectX 11) on the laptops GPU. By lowering the graphics settings I was able to play, but I am much less finicky about lags. With that in mind I thought DOA5:LR based on DirectX 9 in 2015 released on PC would run smooth, but I was wrong. I wouldn't wave off GPU demands so easily anymore. Chances that Sims 3 will run fine however are pretty good, especially when looking at this section from the recommendations:
For computers using built-in graphics chipsets under Windows, the game requires at least:
Intel Integrated Chipset, GMA 3-Series or above
2.6 GHz Pentium D CPU, or 1.8 GHz Core 2 Duo, or equivalent
0.5 GB additional RAM
Both of your options outperform these requirements, but it's hard to tell which level of detail can be achieved and it doesn't look like there is enough headroom for newer games like Sims 4. If I was a Sims fan and had to buy a new computer today to play Sims 3, I'd make sure that it would also run Sims 4 from 2014, which is still based on DirectX 9, has moderate requirements for 2014, but is much more demanding in terms of GPU power. DOA5:LR is still a different game, but let's say I have doubts when I read the following in the minimal requirements:
GeForce 6600 or better, ATI Radeon X1300 or better, Intel GMA X4500 or better
If you still want to go APU only for Sims 3, then it's fine, for Sims 4 I would consider looking at AMD's APU offerings in similar price ranges. They are not very competitive compared to Intel's high performance offerings and their latest desktop CPUs are from 2014, but their iGPUs are said to have significantly more power (1, 2) and the CPU part still manages to run games too.
I think Piotr is wrong when he says:
That way, in years to come, the i7-6700 processor can be much cheaper, not to mention other processors that will come for this chipset (Cannonlake and Kaby Lake).
I would like to see more facts, preferably in the market where you are/the OP is. My experience here in Europe/Germany is that prices for Intel processors are very stable after the spike at launch and opportunities for a bargain offer are minimal if you want to avoid buying used hardware (from users where you don't know how they treat their hardware).
Also buying any board with a Skylake compatible chipset appears more like a bad idea when you look at how many products a chipset family has today and how quickly Intel changed sockets in the last years or which features were missing and were only added to the next generation (no native USB 3.0 for example, and it looks like Skylake and Kaby Lake will have the same thing for 3.1). By now it should be very clear to everyone that Intel is releasing features successively and moving from a tick-tock to a tick-tick-tock model or something different. At any point you will not get the full feature set to be future-proof until the next better thing appears on a roadmap. This is pretty disappointing for long time upgrade strategies, but Intel can relax when it comes to selling single processors currently, they have to focus on marketing entire platforms (all devices where you don't usually upgrade the CPU) and to be fair platforms have increased in complexity so it's not only ill will that we can't go back to the good old Socket 478 or earlier days.