It's all going to depend on what you are doing. The i3 is a hyper-threaded dual core and performance is going to suffer for games that either lack multithreading or where it's implemented poorly. While I don't play EVE, a little research and I saw that it has some threading issues that really affect performance. Star Craft and Sins run fine on dual core processors. I don't know what Total War you are referring to, but Rome II recommends an i5.
For general system performance, an i3 leaves a lot to be desired after you open ten tabs of Chrome and realize you want music in the background as well.
In short, you would probably be best served by getting the i5, either 3xxx or 4xxx series, provided you get a quad core and not some low power dual core chip.