More money gets you mainly much better stills - a bigger sensor gives you lots of resolution and better dynamic range and color (compared with tiny sensors packed with pixels), and, most importantly, the option to shoot RAW. The P&S big zoom cameras do not have that. So, if you care about stills, you need to move up to a big-sensor camera system.
If you do not care so much about portability, the GH3 offers the best video. It's video is better than the EOS M (or all the Canon DSLRs), but its stills are slightly less good. The crop factor of the GH3 helps you with long shots (2X versus 1.6X) for the EOS M for the same focal length.
But, what I am not sure about is the quality of really big telephotos and big zooms for the MFT cameras like the GH3. For the Canon, they are the pro standard - they are superb (if you are willing to pay). And "glass" really matters for good pictures.