The i5 (Haswell) will easily out perform the E300 and cost more.
The E-300 APU did well against the Atom of the time and that was about 2 years ago.
The E-300 is better suited for games like StarCraft ][ where lower FPS (frames per second) don't look as bad. (but the small AMD APUs also won't stutter like the Atoms at the time)
Even with a i5 with HD4400 or HD4600, your choices of FPS games are limited.
You can play older FPS games like Battlefiled2. But it will struggle with newer titles.
If you want to play newer FPS games on integrated IGP graphics, then you need to wait for Iris Pro with eDRAM on Skylake or the AMD equivalent (think Zen late 2015) to go mainstream.