Well, it's beyond me why people think games like Turok are exclusive to PS3, if that is what you're suggesting. It may be because they're forced to promote non-exclusives for lack of Triple A exclusives, in my opinion anyway. The difference between games that are both on each system - the PS3 uses an ever so slightly darker pallet, the 360 has rumble and the PS3 has what is generally considered clumsy motion control.
Don't get me wrong there are some good points for the PS3, but I think they're far outweighed by the good points of the 360. The major one being the much larger games catalogue. Right now, it's impossible to guess which system will have the better exclusives in 2008, as most games that have been announced are for both consoles. However, the 360 already has two years of awesome exclusives behind it, some of which are fresh out, some of which are from nearer the launch but are still very much a sight to behold. What the PS3 does have in exclusives aren't that great. Trust me, I've played the majority of them on my brothers machine. Resistance is a mediocre FPS, of which the 360 has the best ever collection of, Motorstorm is a fairly fun game , but the graphics are overrated and it's easy to grow tired of it. Heavenly Sword, well, you might as well have God Of War 2 as it is considered by fans and critics alike to be a similar but far superior game. Lair is apparently difficult to control, although pretty, and thought by almost all magazines I've read to be awful. Ratchet and Clank seems like a great game and I should be getting to play it around Christmas, but if you've played any or every installment so far, prepare for much of the same. Uncharted is another one I'll be playing around Christmas. Right now, I don't see what the big deal is. It seems like Tomb Raider to me. Or, how many have dubbed "bloke raider". I'll probably give an update once I've played it.
Personally, I don't have Xbox Live. It is very nice to have, yes. It does make your experience more pleasurable, yes. But it isn't really necessary. There are plenty of single player games on the 360 that offer enough depth that you don't need online. The only problem is, bastard, cock-sucking developer's stopped integrating local play into many games, and so it's getting more and more difficult to get your mates around your house to play a game. That's a problem for both consoles though. How I miss the days that Time Splitters ruled supreme on PlayStation 2...
I think that maybe your parents should research into Xbox Live before completely saying no. If you get a premium or elite Xbox, you get a month of free play anyway, and after that it's only forty pounds a year for it. That works out at £3.33 a month, hardly as expensive as some would have you believe.
Now, you might say I'm biased. Well, that's an inevitability, everyone's biased. I can argue, however, to the degree to which I'm biased. I'd say not very. I often play the top games on other consoles round friends houses. In fact, I'll be getting a Wii soon. I've had the two PlayStations previous to the third, so you can't say I'm brand loyal or have some sort of grudge against Sony. In actuality, I think the original Xbox was an overpriced pile of shit, with only a couple of good games released each year. I'd say it's more comparable to the PS3 than the new Xbox.
I will say this though, if you want a cheap blu-ray player, go with the PS3. It undermines the entire concept of a games machine, but if what you mainly want is a cheap blu-ray player, there's no point shopping anywhere else.
Either way, have a Merry Christmas!