Better, yes. But better enough to warrant the cost, that I can't answer.
Keep in mind that what you are asking for (freezing action and getting it up close from the stands) is a lot. Arguably too much. But that depends on your definition of acceptable. In order for me to get a shot that I consider great, from the stands, would require a very, very expensive lens. But if there’s one thing that I’ve learned from being a photographer – the average person doesn’t look at a photo the same way a photographer does.
Lets deal with the easy stuff first: a dSLR is much faster than a point and shoot. Modern P&S have gotten much faster, some are quite fast, but their autofocus is still slow, and there’s no point in having 10 pics of an out of focus subject. dSLR can take multiple shots a second, and they can even re-focus in-between shots. Additionally, the shutter lag – time between pushing the button and the shutter dropping, is quicker (though some P&S have gotten really fast). All these advantages make dSLRs much better equipped for sports.
Freezing action requires a fast shutter speed. Easy for just about any camera in good light, but as light fades you’ll start to see the difference between P&S and dSLR. The sensor in a dSLR is much bigger than most P&S, so it can collect more light, which means it can use a faster shutter speed (in a sense). But this can only take you so far, to really reap the benefits of a dSLR you need good lenses. More specifically, you need lenses with a wide aperture to let in a lot of light. Again, outside in the sun it’s not such an issue, but freezing action of indoor sports is pushing the limits, and it really can’t be done well (subjective) without a good lens and preferably a good camera. Will a Rebel with a 55-250 kit lens perform better than a P&S with indoor sports? Yes. Will it provide acceptable results for you? I can’t answer that. I will say that getting a Rebel with the two kit lenses is a big step up and I think you could have a lot of fun, and learn a lot about photography with that setup.
One last comment: you’re correct, STM is primarily for video. I would try to find a refurbished version of the previous version of the 55-250 and save a bit of cash.
