XBox 360 has better graphics and specs.
Nice try, but this is wrong and wrong. The PS3 is more powerful, however graphics wise, they are both as bad as each other.
Either system is good. I have all of the current gen consoles and really they are all decent (except the Wii, not touched it in about a year and half). I use my PS3 most, however that isn't because it is better, it is because it is set up to the TV in my bedroom, so I will watch films/shows through it in bed. The 360 is in my living room where we have cable, so the Xbox is just for games, which I use my PC for mainly.
Graphics and performance wise, no difference between the two.
Games wise, that is personal preference. The only 360 games I am bothered about are the Gears of War games, with PS3 I prefer GT5 to Forza, I love inFamous and Resistance so games wise, I would take the PS, but like I said, it is personal preference. Look at the games and see which appeals to you more.
Consider too online. Firstly with gaming, it is free on PS3 whereas it is subscription based on the Xbox. Some argue that the 360 online is better, however I think that depends on which system your friends have. If all your friends are on a PS3 and you have an Xbox, you have nobody but the crying 12 year olds to play with, so which will be better then? Likewise with the consoles swapped.
There is a subscription option for the Playstation store, however it is much cheaper (I just paid £30 for 12 months) and the benefits are greater imho, seeing as how you get free games from it and large discounts on others.
Consider other services too. Whilst the 360 does have the likes of Netflix and LoveFilm so you can stream TV and films, you have to be an Xbox Gold subscriber to use it, so on top of your monthly payments to Netflix/Lovefilm, you have to pay Microsoft to use it on your console. The PS3 on the other hand has them as well and you can use them for free (after the service subscription to Netflix or Amazon).
I think it really comes down to what you want from the console:
Is it going to be a media centre rather than just a games console? - Go PS3 every time
Is it going to be used just for games? - Either, they are both equally as good. Look at the selection of games and take whichever is better for you