The consoles are different and custom made, with 8 GB VRAM and so on, the processor isn't really worth mentioining however it gets 60 FPS in a lot of titles which is impressive even though majority of console gamers never cared about FPS anyways unless their game was moving like a slideshow. It's preference and if you don't need to play at the highest resolution you could compromise and lower the resolution and sit a foot further back and you won't be able to tell the difference between the two, not to mention lowering graphics settings.
The 8350 is a very solid CPU and is often compared to the i7 4770 in workstation benchmarks which is impressive but it's single core performance isn't the highest, however you'll have no complaints, and since you're on a tight budget it makes a lot of sense. However, if you won't edit videos, or heavily multitask then a locked i5 may be more suited for your needs.