Most people start with a digital compact, but if they get serious about underwater photography they sooner or later start to think about an SLR. So, should you trade your compact in for an SLR outfit? SLRs are a big jump from compacts, and it's worth thinking about what you stand to gain and lose, and how important these things are to you. Here's a summary of the pros and cons...
SLR Pro's
Image Quality is better - look closely at SLR images and you'll see better dynamic range and tonal smoothness with less noise, especially if you use higher ISO settings. This is down to the physically bigger sensor - a typical compact sensor may be 7mm x 5mm, an SLR sensor with the same pixel count may be 22mm x 15mm, or even bigger. This means the individual pixels can be larger and further apart, making it easier to control image noise and tonal distribution.

The top image is from an 8 million pixel SLR at 100 ISO, the bottom image is from a 5 million pixel compact at 50 ISO. Both are in-camera JPEGs with no processing except levels adjustment and cropping. The SLR image is less noisy and the tones are smoother. These effects are a combination of pixel count, sensor size and image processing, but aren't necessarlity important in prints to A4 or smaller - these pictures are the approximate equivalent of A2 prints, and larger prints will be viewed from farther away. Try standing four or fve feet from your screen and see what they look like then.
Noise is lower

The best compacts on the market today will give near-SLR quality at low ISO settings, but increase the ISO and the differences really start to show. The trend to higher and higher pixel counts doesn't help with this, but that trend looks set to continue as it's easier to explain the benfits of more pixels than low noise at high ISO
Lens choice is broader - you can get wider wide-angles and properly designed macro lenses.

The larger left hand image was taken using a 10mm fisheye (The excellent Tokina 10-17mm fisheye zoom) on my Canon. I have an old manual Russian-built Peleng 8mm fisheye that gives me an even wider angle of view. The shot top right was a compact plus fisheye, bottom right a compact plus wide-angle adapter
SLRs operate more quickly - press the shutter release and the picture is taken, whereas compacts first have to focus, then get ready to operate the shutter, then actually take picture, by which time fish will be showing you their tail-fins! Shutter lag on compacts is getting shorter, but it's still there, and shouldn't be underestimated. Yes, you can get shots of rapidly moving critters, but your throw away rate will be much higher with a compact than an SLR.

The first time I used my brand-new SLR was on a southern Red Sea liveaboard. By the end of day two I was ready to heave the damn thing overboard and have done with it, and took it with me on the first dive of day three more out of duty than expectation. As we got back to the boat a pair of Oceanic White Tip sharks cruised past, and this was one of a series of shots I got. I would have got less good results with my compact because it works too slowly - the one subject I've never really caught has been the seals of the Farne Islands, they move too fast for the comapct to focus and shoot. This shot, and the other shark pictures, are the reason I persevered with the SLR and didn't put the housing on eBay the day I got home!
SLR Con's
Size and weight

An SLR will dominate your dive and rip your arms from their sockets on long RIB rides. To be honest, you do get used to it, and only notice the camera when it isn't there, but the first time you take a housed SLR underwater you'll wonder why you bothered. You might have problems meeting weight limits for airline trips as well, until you accept that a spare t-shirt is less important than your macro lens. The full compact rig shown on my compact page weighs less than 3.5kgs, including all the necessary batteries, chargers, leads and so on and fits in my hand-luggage. My SLR outfit weighs 12.5kgs, and means I need a separate box for airline trips, and sometimes, depending on how good a day the check-in staff are having, means paying excess baggage.

Ready to dive - compact with wide adapter lens on left, SLR rig with fisheye dome on the right
Cost - any basic housed SLR system will set you back at least twice the price of a comprehensive compact outfit, and three to four times that much when you've finished buying extra lenses and ports. The Olympus compact outfit shown here would cost around £850 to replace, the Canon SLR rig would cost £2500 to replace, and bear in mind my strobes came from eBay and the actual camera is the base model of the Canon range!
Image Quality - SLR images are better, but, and this is important, for most people most of the time they won't look better because they'll be viewed on low resolution computer monitors or made into relatively small prints, and besides that, they're really only a little bit better in absolute terms.

It's very difficult to make meaningful comparisons from pictures on the web - pictures have to be downsized and subtleties are lost and screen resolution isn't that great, but even so the SLR shot here is visibly better quality than the compact shot, the question is if that quality gain is worth it to you?
Modern digital compacts are capable of superb results. Digital SLRs are even better, at a cost measured in cash and size/weight/complexity. Which you choose is up to you, but whichever it is, the pictures you take will be limited more by your ability as a photographer than the equipmet you use.

In the water, there's nothing much to choose between compact and SLR rigs in terms of weight thanks to the bouyancy of the larger SLR set-up, but handling the bulkier SLR rig takes more time and practice