The SX10 and the G10 are both very nice cameras (at least by spec), and you can take some very nice pictures with them, but neither are suitable for "professional level" photography.

The SX10's real benefits are a hot shoe, which allows for a good quality flash to be added (which would actually probably cost about as much as the camera), and a 20X Zoom.

The G10 also gives you a hot shoe, you lose the Zoom capabilities but add the ability to capture in RAW which is a real benefit for editing the pictures. Also, since it does not have quite as large a lens and form factor, the G10 has the ability to fit in a (large) pocket.

But they are both cameras with small sensors, and as such, the noise levels on them are considerably higher than on even an entry level dSLR.

With an estimated street price of $499, the G10 is only slightly more expensive than say the Olympus E-420. E-420 is not the best dSLR on the market, but the Four Thirds Sensor is considerably larger, and will give you much better results than any point and shoot camera, and would not be a bad starting off camera.

Alternatively, if you are afraid of making an investment in lenses with Olympus that you may not wish to stick with, you could also look to some of the larger camera sellers that offer used dSLRs at low prices, so that the investment in lenses you make can go with you when you step up later to a better camera body.

As to which one of the two cameras you originally listed is "better" well, it really depends on what you want to photograph. They have different bodies and styles and suit different purposes.