Actually, there are benefits of AppleCare. According to Squaretrade's information, they don't cover any accessories, such as power cables or connectors. Applecare does. So if you have a MacBook Pro and your power cable dies, with Applecare you get a replacement for free. With Squaretrade, you have to buy one, which costs $79 at the Apple Store.
AppleCare can be purchased on refurbished Macs. Squaretrade won't let you do that. You can purchase AppleCare anytime during the first year you own your Mac, and it will kick in after the one year warranty ends. Squaretrade states that their warranty starts on the date you purchased the item, so it's running concurrently with the regular Apple warranty. And from what I saw on Squaretrade's website, they pay for accidental damage only if you purchase the Accidental Damage from Handling coverage along with your warranty.
Squaretrade will cover your equipment up to the purchase price. So, if you purchase a $999 MacBook Air, any repairs or replacements that they do over the lifetime of your warranty can only cost up to $999. Anything over that and you're out of luck. They consider the contract fulfilled, even though you haven't actually reached the date it's supposed to end. If your computer can't be repaired and needs to be replaced, or if you've had the same problem repaired 3 times over 12 months (lemon law) and they replace it, that's it for your contract. They specifically say "Upon replacement of a Product, We will have no further obligation to repair or replace the replacement Product and You will not be entitled to make any claims under this Agreement for its repair or replacement." AppleCare doesn't say that, at least not anywhere I can find. I know of several people who have had machines repaired or replaced multiple times, without worrying about the total cost.
Does Squaretrade cover the monitor, keyboard, mouse, Airport Base Station, Time Capsule, etc? I couldn't find info on that on their website. AppleCare covers them, if they're used with your covered equipment and were purchased up to two years before your Mac purchase or during the terms of your contract.
So, no benefits you say? Hmmm...I'll stick with AppleCare