All three of Sram's top groups are excellent and very similar (Rival, Force, Red).
You can save a bit of weight going to the more expensive group, but not a whole lot.
As of 2010 all three use carbon fiber brake/shift levers (and are 100+ grams lighter than comparable Shimano). The weight difference between the Sram levers is in the 10s of grams per piece... not much. 2010 Rival have a matte clear finish on them that might be harder to touch up. I think both Red and Force are gloss finish, which touches up very easily (in the traditional way... with clear finger nail polish

). Purely cosmetic consideration, of course, but levers always seem to get scratched a bit in use.
The Sram brake calipers in these three groups differ in finish, primarily. Rival are black painted or anodized and about 10 grams heavier per caliper. Both Red and Force are polished and clear coated, with Red slightly lighter still thanks to some Ti parts. I think the Force finish looks a little warmer (I'd call it "Ti-like"), while the Red might be a little cooler ("chrome like" or bluish).
Some folks prefer the modulation and clamping power of Shimano brakes over Sram. Personally I find them very similar, but I swap out the brake pads for Kool Stops in either case (Ultegra brake pads in particular used to really suck... I hear they are much improved for 2010 but haven't used them). One small thing.... All three Sram and all three Shimano (DA, Ultegra, 105) have click stops on the release lever that opens the caliper to remove the wheel. Some third party brakes don't (for example Tektro, as well as Cannondale or others made by Tektro). It seems a really minor thing, but personally I prefer the click stops.
Some of it comes down to aesthetics. For example I chose to use mostly Rival group (2010) on one bike because of it's predominently black finish... I just think it looks best on that particular frame.
The crankset is the biggest area of potential weight savings and the lightest one, the Red, is also the stiffest of the three Srams. The Rival is the heaviest of the three Sram cranks because it's aluminum while the other two are carbon fiber. So if there is one place to upgrade, it might be the crank. If stiffness is important, go with the Red. If not, go with the Force. There's not much difference in weight between these two.
Red uses more titanium hardware and parts to cut weight. The front der is one place this might not work out too well. Some folks like the Force better on otherwise Red equipped bikes, because they feel the shifting with the Force FD is more certain... Perhaps because the Ti cage of the Red is a little flexier.
The Rival rear der uses an aluminum cage and body. The Force and Red have some carbon fiber parts on the cage to lower weight.
Folks do have preferences about the chains and cassettes. I've been using several Sram cassettes (1070, which are shared by Force and Red) along with their chains (1090R, which are Red-level) and am happy with them. I have a Sram cassette/chain set on an otherwise Ultegra (6600) equipped bike, and it works just fine and runs quietly. But, Shimano 105/Ultegra cassettes and chains work fine, too.
Some say that the Sram cassettes and chains are noisier than Shimano. With all adjustments dialed in and good chain lubrication, I don't notice any real difference.
Some Sram chain users prefer to use a joining link such as the KMC, rather than the provided Sram Powerlink (which
technically is designed for single use). But some prefer the reusable links on Shimano chains, too, rather than Shimano's pin replacement method.
I've been tempted at times with the low, low weight of the Shimano Dura Ace cassette... But that's achieved by using a cluster of titanium cogs, which means it costs a lot more and wears out a lot faster. So it's probably not the best choice for a recreational rider or commuter. Sram's Red level (1090) cassette is also very light weight... I don't know if that's also thanks to the use of a lot of Ti though.
If anything, the three Sram groups are a little less forgiving than Shimano counterparts when setting up and adjusting. For example, I think the Shimano rear ders are more forgiving of slight misadjustment. All three of the Sram front ders need to be carefully aligned and positioned, per the instructions, and the cable tension in particular needs to be just right. One suggestion... To facilitate proper front cable tension install an inline cable adjuster on at least that FD cable (like most, the RD has a barrel adjuster, so an add'l inline adjuster is more optional).
Assuming you are using the now common external bearing cup type bottom bracket, be aware that the Sram crank's spindle and bearings are not cross-compatible with Shimano and most other cranks/BBs. Sram uses two different size bearings and the diameter of the spindle is slightly smaller on the non-drive size... Most others use the same size on both sides and a spindle that's the same diameter at both ends. Just looking at them side by side, they appear the same... But they're not. (If your bike happens to use BB30, this is not a consideration... Unless you're using an adapter to fit up an external bearing-type crank.)
I don't have any experience with Sram's newly introduced 4th tier group: Apex. So I haven't mentioned it much here. It's gotten a lot of good reviews, from what I've seen. I guess Apex (10 speed) is positioned to compete with Shimano Tiagra (still 9 speed, I think). AFAIK, Apex uses aluminum brake levers and an aluminum crank.
I recently compiled the manufacturer's claimed weights of Shimano and Sram 2010 groups, all with a standard double crankset (53/39) and a common cassette (11-23T). (A compact 50/34 crank with a matched, shorter chain should save a wee bit more). Here's what I found:
Sram Red group: 1940 gr.
Shimano Dura Ace group: 2045 gr.
Sram Force group: 2107 gr.
Sram Rival group: 2200 gr.
Shimano Ultegra group: 2313 gr.
Sram Apex group: 2358 gr.
Shimano 105 group: 2545 gr.
Shimano Tiagra group (9 speed): N/A (Shimano doesn't publish some component weights)
I do take all these claimed weights with a grain of salt. Most manufacturers note that their published weights are "averages" or otherwise disclaim them a little. I recently weighed a "180 gram" labelled Fizik saddle and found it's actually 235 grams! Sometime when I have nothing better to do, maybe I'll weigh more of these components myself and see how accurate some of the claims really are.... Or maybe I won't
The two primary places significant weight is saved are in the cranksets and the shift/brake levers. Note: some have made it work, but generally you shouldn't mix Sram shifters with Shimano deralleurs, and vice versa. OTOH, as noted earlier, Sram chains, cassettes, and chainrings seem to work just fine with Shimano... and vice versa.
One thing I'd suggest if at all possible, check out the different groups (Sram vs Shimano vs Campy) on bikes in a store. Across the Sram groups, they're very similar. But Sram vs Shimano (for example), they feel a little differently ergonomically, with different shape hoods, etc. Some prefer one over the other. They also shift a little differently... Sram uses one lever for both up and down shifting, and tends to be "crisper" or "snappier", for lack of a better term to describe it. Not saying better or worse ... Just
different and some folks prefer one over the other.
I'm currently riding:
1. Ultegra (6600) equipped bike (with Sram Force/Rival 1070 chainrings and cassette, 1090R chain)
2. Rival equipped bike (except for Red crankset and 1090R chain)
3. And am gradually building up a Force (2009) equipped bike.