The size of the camera body has little to do with the quality of the image taken. I'm assuming capture the disc means follow the disc in flight, and neither of these cameras are going to really be great for it. The qualities you're looking for in a camera (lightweight/compact) actually are the opposite of what you want for long-distance tracking. Here's why:
1. If you're not a SEAL Team sniper, your hands are never steady. The weight of a camera acts as a dampener of hand-shake. Lightweight cameras shake with your body*
*This can (and should) be reduced by using a tripod*
2. Fixed-lens cameras (the price range you're looking at) use digital zoom, not an actual moving lens. Thus you're effectively lowering the quality of your image because you're just taking a pixel and zooming in on it. The sensors in those cameras just aren't that great, and you'll see pixelation. Digital Zoom also makes hand shake worse...imagine it like using a magnifying glass on a painting.
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I would say that the bare minimum for getting a quality image (non shaky/blurry/crap) while tracking a disc is a DSLR, and that still takes lots of practice because those cameras aren't meant to shoot sports...but it's less of an impediment than a compact fixed lens (aka "Pocket Camcorders")
Now...to complicate things. I use two small cameras to shoot disc golf - a Kodak Zi8 and a GoPro Hero. However, I don't usually try to track anything more than a putt with them, because it's just difficult to do and doesn't usually look great. These small cameras however, will do smooth slow-mo and are easy to get up close and personal with your subject because they're small and compact.
There's plenty of ways to make disc golf video look really good without tracking flight, so use the advantages of your camera and I'd suggest just trying to find creative ways to shoot new angles and things we haven't seen.
Hope this helps...and let me know if I can clarify anything I'll be glad to share what I've learned (through my own screw-ups) so you don't have to spend time making my same mistakes, lol.