This is a little late, but it depends on your preferences. I prefer computer's so I'm with Mark, but I would not advise a low I5. I'd say 4670/4690 now that it's out or AMD 8320 (8 cores, 3.5Ghz, often on sale on one of the sites for around $130, I got my second one for $105, best price/performance in the world, IMO).
The 270X is an updated and rebranded 7870, which is the same GPU the PS4 has (90% sure Assassin's Creed 4 looks better on my 270X than it does on the PS4),
We need your computer specs, if you have 2GBs of ram, just get the PS4, if you got at least 8 or 16+ then the computer is worth upgrading. I was suprised to find my 270X needed more power than my 600w or 650W (these were "peak" ratings) PSUs could give, so the power draw needs to be considered.
Either way you'd have `1080P, PS4 won't go lower, it also only has a HDMI output.