The first half of this video was shot with the $150 SX130 IS, the second half with the $500 Canon T3. Changeover occurs around the 45 second point and is quite noticeable. here are the differences I noticed:
SX130 has brighter colors, better high-frequency sound pickup (makes sound brighter and less muffled) and less wind noise. Motion also appears slightly less blurred.
T3 seems to have better detail resolution but the subdued colors are less eye-pleasing. The T3 was set to not adjust focus during the shot so focus was locked for each shot. I used the "quick-focus" setting where the mirror flips up to set focus before recording starts. Both videos were recorded at 720p. Both cameras were handheld. I used the zoom a couple of times on the T3 but not at all on the SX130. The T3 takes much better photos, of course.
Conclusion: for this application I think the SX130 is the better camera. The longer zoom lets me get closer to the action, the stabilization works better, and the sound quality is better. The autofocus is also better suited to filming sports.