Ok if you used a SX20 then you experienced 20x zoom. Did you use it alot or even every so often?
See the upside of the cameras like the GH2 and GH3 is you can still get reasonable zoom with light kit.
I'll try not to get too complex.
But all cameras are measure against 35mm film technology in terms of focal length.
So your SX20 could go from 28-560mm (on 35mm film equiv).
Now the GH2 are micro four thirds. So they have 2x factor. That means you need 280mm to give back a view of 560mm (35mm film equiv) .
So a lens of 14-140mm gives you 28-280mm (35mm film equiv). Bit shorter than the SX20.
But if you feel you don't need the 560mm or 20x zoom range then you should look at a lightweight dSLR as well. But need to know it will have a optical view finder which is different to your SX20 and the GH2/GH3.
Best thing is find a store stocking say a Nikon D3200/D5200 and the GH2/GH3 but raise the issue of longer focal lengths and how the camera feels and weight. To get a D3200/D5200 to give 560mm it has a 1.5x factor that means 373mm or probably a 400mm. That might be a expense lens.
PS:AP have reviewed the GH3.
http://www.amateurphotographer.co.uk...dmc-gh3-review