Whether you choose an Xbox 360 or Playstation 3 depends on what you are looking to get out of the experience. Are you using this for multimedia and entertainment, or pretty much excusively for gaming? Do you already own a blu-ray player? What type of games do you like? Are there any specific games you are interested in that may be exclusive to one console or the other? What do your friends own?
The Playstation 3 is a great "all-purpose" console. It has a blu-ray player, internet browser, streaming capabilities, bluetooth, etc. If you have a wide range of activities you are looking to be able to do with the one machine, this is the one for you. There are also some really nice exclusives like Uncharted, Killzone and God of War. There is also Playstation Move, which uses a system similar to that of the Wii, but is more precise and IMO, enjoyable.
The Xbox 360 is a really great system that is specialized in gaming. There are lots of other things you can do with the 360 (like Netflix and YouTube, as well as streaming from your computer wirelessly across your home network), but it is first and foremost a piece of gaming technology - moreso than the PS3, IMO. There are really great exclusives like Gears of War and Halo. It also makes use of the Kinect, which allows for completely hands free interaction with the console as well as voice recognition to make searching for videos and movies on apps like Netflix and YouTube easier.
Both the PS3 and the 360 have wireless built-in, but it's worth noting that the 360 uses a wireless N adapter and the PS3 is still rocking the outdated wireless G adapter. Ultimately, this shouldn't make a difference in terms of performance for online gaming as most peoples' service providers don't offer internet speeds that will be higher than you can get with a G adapter.
In terms of overheating, both the 360 and PS3 have their issues, but ultimately it comes down to you. These are both essentially high-powered computers designed for specific purposes, and crammed into a small, sleek casing. They WILL produce heat. You can't have that much tech crammed into that small a space without making sacrifices for cooling. Ultimately, it's up to the consumer to be smart about placement of the console in order to prevent overheating. I have had my Xbox 360 for well over three years, and have NEVER had a mechanical issue with overheating, RROD, E74 or whatever. It's still running as good as it did on the day I bought it. I keep my Xbox out in the open so there is lots of airflow, and it never gets very hot, even after long periods (like 6+ hours). The PS3 gets quite hot, but it is built solidly to be able to withstand that level of heat, and I've never had an issue with overheating or YLOD with mine.
Both are solid machines, but if you do something stupid like stick it in an enclosed space, or on a shelf where there is nowhere for the heat to go but to the back, where it stays and festers, then don't be surprised if it breaks due to overheating (this goes for PS3 and 360 alike). If you take care of it, keep it clean and keep it in an area with good airflow, your console should last you for many years.
Finally, do not make the mistake that because the PS3 uses blu-ray, the games must automatically be better in terms of graphics for cross-platform games. It's the hardware that makes the difference graphically, and you'll see those differences in the exclusives that are designed to specifically take advantage of the hardware of the console it's made for. The advantage of blu-rays is extra storage capacity, so more can be fit onto a single disc, but beyond that, for cross-platform games, there is usually little, if any difference between the two. The main difference you may see, depending on the game, is the 360 version will use more than one disc as it uses DVDs instead of BDs. The overall game will be the same.
I own both systems and use the 360 as my gaming centre. I use my PS3 for blu-ray movies. Both are great systems and can do great things, and if you take care of them, will last for years. The biggest factor, IMO, for deciding on a console is what are your friends playing? Choose the system that most people you know are playing, as you'll get a much more enjoyable experience playing with your friends than playing with strangers.
I hope I've helped narrow down the key similarities and differences between the consoles and I wish you luck in your decision. It's a great time to be a gamer, no matter what system you choose.
JB
One more important thing, which I think deserves its own post as opposed to an edit, is that if you are buying your new console from Future Shop, get the product service plan!
I don't normally make any recommendations one way or another with regard to the PSP, but in the case of gaming consoles, it's a no-brainer to me. The PSP in this case goes WAY beyond the console itself. It also covers the accessories in the box (controllers, headset, video cables, etc). Think of how much just one of those things costs. The PSP might cost you an extra $70-$80 on top of your purchase price if you go for the three year one. If a controller breaks, you get an over the counter exchange, no questions asked (in my experience). After replacing one controller and one headset, my PSP had paid for itself. I've replaced another controller and headset since then (I game a lot 
). If you get the PSP with a console, within the first three years just on accessory replacement alone you will likely be saving a lot of money. If you get one of the Kinect or Move bundles, those would be covered as well, along with everything else that came in the box. It might seem like a lot of money to put in when you are already spending that much, but in reality, over the next three years you could be saving yourself hundreds of dollars.
Cost breakdown
Xbox Controller - currently $20 off
These are the main expensive items that come in the box, but all cables and such that come in the box wouldn be covered as well, and if, over time these things break down, then you will be able to bring in the defective accessory and exchange for a new one.
I cannot stress enough that if you are a person that will be doing a lot of gaming, this is something you really need to consider, one gamer to another. I'm not a Future Shop employee, I'm not going to make anything off of any purchases you make or whatever like that. I'm just a regular customer sharing my experience with the PSP for consoles, and unless there are drastic changes made to the terms of the PSP, I will always recommend it to people. I have yet to see another extended warranty that comes close to offering the same level of protection and value that is offered by Future Shop.
JB
You know what annoys me about xbox? The stupid points system! So 400 points = five dollars, but this game costs 1000 points, but wait I can only buy 800 or 1200 points at a time so if I buy these points, subtract the difference and carry the one... but wait, now for some reason I have 267.5 points left, and I need a complex algorithm to figure out how much I just paid for that add-on content 
On psn a buck is a buck, and if you want to buy something, you buy it straight up, no adding additional points by increment to overshoot your total!
Overall I prefer PS3 over xbox for multi-platform content etc, but we're pretty much debating coke v. pepsi here. It's 5% personal preference, and 95% marketing 
