You're going to get a lot of die hard SRAM fans, SRAM haters, Shimano fans, Shimano haters, and the inevitable "Campy is best" crowd.

SRAM (from lowest to highest): Apex, Rival, Force, Red
Apex is a bit different in that it supports long reach brake calipers, medium (or is it long) cage rear derailleur. Mostly aluminum bits. Apex promotes the "Wi-Fli" where you run a compact crank up front, and an 11-32 cassette given you wider gearing than a triple. Apex cranks are solid I believe.

Rival is the best value IMO (except for the brakes ... you get slightly more adjustability on the Apex, Force and Red brakes). Best deals can usually be had on Rival. Rival adds carbon fiber shifters (aluminum paddles) and hollow cranks.

Force is a step up, although no features are really added. Shifters have different graphics, are supposedly lighter (but real world numbers dispute that), they use CF (different finish than rival) and Magnesium paddles. CF on the rear derailleur cage. Crank becomes CF as well. Brakes are identical to Red except for color

Red is the top of the line, you get Zero loss shifting on both the front and rear (all other SRAM groups are front only), and lots of CF + weight reductions all around. The Red cassette is machined making it one of the nicest cassettes out there. The FD is titanium, some have had flexing issues and use Force/Rival intead.

Summary: No major differences aside from material, weight and Zero loss on the front for red. Rival offers the best bang for the buck by far. Most of the extra weight of Rival/Apex are in the crank, if you look at the specs you can figure out which bits to upgrade if you care about weight.

Shimano's offerings are a bit more complicated: Sora, Tiagra, 105 (5700), Ultegra (6700), Dura Ace (7900).
I'm not sure how many speeds Sora is using, but Tiagra is 9-speed while the rest are 10 speed. My understandind is that features are the same with weight differences/smoothness from 105 to Dura Ace. Many have said that 6700 shifts as well or nearly as well as 7900 Dura Ace. You also have the electronics Shimano groups (well groups in a few months when Ui2 comes out), but that's another matter. 105/Ultegra offer the most value.

Differences: Shimano uses two levers for shifting while SRAM uses a single paddle. You'll get used to either. Shimano is a bit heavier, SRAM is a bit lighter at the same price point. Shimano shifts a bit smoother, SRAM shifts loudly and firmly. This of it as driving a sports car, vs. a more luxury sporty car (Bugatti vs Ferrari or something) ... they're both great just different, they both do what they're supposed to.

As of the latest revision, Shimano is now using directional chains and a different brake pull ratio than SRAM (previously you could interchange brakes). Cassettes are interchangeable, with some finding that SRAM bites less into aluminum freehub bodies.

Overall, you won't go wrong with either. Ride both, see which you prefer and pick one. They've both won TDF top spots, good enough for TDF riders, good enough for us