None if you are using four, or up to four. Once you hit I7 territory and above though it tends to suffer from issues which the only fix for is a rather crude core parking hack.
It's not an issue in software that doesn't care for cores, but in certain software an I7 is considerably worse than an I5.
Windows 8 got a complete rewrite so handles multiple threads far better than 7, and also fully supports the AMD FX architecture so if you are running for example a FX 8 core you can get up to 15% more performance in highly threaded apps and games.
Not an issue unless you're a core whore like myself. My lady's rig for example runs a 8c 16t Xeon, so 8 was a must. Due to the core handling things like multi tasking are far better too
8 was not just 7 with an Ipad glued on like many people accused it of being. Underneath had a massive amount of work done on it also.
I turned off hyper-threading on my i7 a long time ago, many games ran worse with it enabled, in some cases quite visibly so.
One of the first and best fixes for stutter in Battlefield 4 is 'turn hyper-threading off'.
i5s are generally the CPU of choice for gaming PCs.