I personally recommend a gaming pc, as new releases will stop releasing on the PS3. IMO, get a PC and you can save money by downloading games from online digital sales. BF3 was free last month on origin, TF2 and Planetside2 are free to play, games like AC4 sometimes can be found on sale for $35. I would buy a PC and save money through digital sales, and use the money to upgrade the pc over time.
If you can, I STRONGLY recommend getting some used parts, considering your budget. Parts that should be ok to get used are: ram, hard drive(may fail, must run a hard drive hdd test before buying), case, monitor (got a 1080p monitor used for $50CDN(~$45 USD), accessories (keyboard+mouse+speakers), wifi adapter and similar). Heres what I suggest getting. Price doesn't onclude OS:
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD A4-6300 3.7GHz Dual-Core Processor ($49.99 @ Newegg)
Motherboard: Gigabyte GA-F2A55M-S1 Micro ATX FM2+ Motherboard ($34.69 @ Newegg)
Memory: Corsair XMS3 4GB (1 x 4GB) DDR3-1333 Memory ($34.99 @ Newegg)
Video Card: XFX Radeon R7 260X 1GB Core Edition Video Card ($89.99 @ Newegg)
Case: Logisys CS206BK ATX Mid Tower Case w/480W Power Supply ($32.34 @ NCIX US)
Keyboard: IOGEAR GKM502 Wired Standard Keyboard w/Optical Mouse ($10.40 @ B&H)
Other: 250GB Refurb Hard Drive ($24.99)
Other: USB Wifi Adapter Ebay ($2.11)
Total: $259.50
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-07-27 00:42 EDT-0400
You will have to go slightly over your budget though. Check your craigslist or local ad site for used parts. I got a 1tb hdd for ~$30, and 8gb ram for ~$45 (there are some good deals out there).
If you really want to buy an PS3/Xbox 360, I recommend going on craigslist. I can find xbox 360's in my area(large city) for $40CDN(~$35 USD) and PS3 for $70CDN(~$60USD) with possibility of negotiating down a few dollars. PS3 should be better than xbox in your case; PS3 online is free, xbox live gold is not (online is like 90% of the game IMO(at least in call of duty)). I have an PS3 and I love it. As previously stated, I recommend PC as the PS3 and 360 are at the end of their lifetimes, so new games soon won't be releasing anymore on them. PC can also function as many other things (as a pc obviously, as a htpc, use as steambox, web browsing, media player, etc.).
Looking at the recommended specs, that PC should be able to run COD: Ghosts and similar power games at high or ultra settings at 720p, compared to lowest settings on PS3 and xbox 360.
Good Luck!!!
Hope I helped.
EDIT: Whats your monitor resolution, and what games do you want to play?