I'm gonna get flamed for this, but here it goes.....
Xeons: Pending on the model / version / core count etc, it will perform as good as any of the Intel i series of cpus in most cases. The difference, well, I'm not sure anymore due to some of the later Q2'15 Xeons like the Intel® Xeon® Processor E3-1265L v4 which has on board Iris pro 6300. The only difference I can see is higher memory bandwidth up form 25.6 GB/s to 29.8 GB/s for the Xeons.
i3/5/7: hyperthreading for the i3/7, i5 with out. Lower cost, lower bandwidth cpus compared to the Xeons, not much to say really, pick the socket, mainboard to suit, and correct ram and get building. I would only really look at higher end i3 or K series for the i5/7 (thats my opinion). The onboard is OK, but don't try and game on it, doesn't cope too well.
What you really need to figure out is:
1. Is it a working station computer, with little gaming on the side?
2. a gaming rig?
3. very light gaming, mainly internet surfing, HTPC, etc?
4. a home or game server?
Options 1 & 4 I would recomend a Xeon over anything else. This is due to more often a higher core/thread count, and higher over all memory bandwidth, and the more likely hood of multithreaded applications running.
And i series for 2 & 3 due to lighter single to dual core or threaded workloads (gaming and trolling on the interwebs).
Truth of the matter is, What ever the cpu you have, it will perform all the tasks you ask it to do. How efficently it does it, is something else.