For a "snapshot" type camera, I would consider a move from 35-210mm (AS650) to 28-140mm (G11) as a pretty important upgrade. Yes, you do lose some reach on the long end, but you gain a LOT on the wide angle for close range and "party" shots which is what this type of camera is typically used for. It also gives you a significantly wider angle of view for landscape and panoramic photos. Take a look at the first two photos in
this link to see an example of the difference you will get between the two. Now, if most of your pictures are taken at the long end of the zoom, then the G11 may not be for you...
Since you didn't specify, I'll have to guess at what might be the other important changed features that you are looking at:
The continuous shot speed on the G11 is significantly improved. The actual burst speed is almost identical at 1.16 FPS for the A650 and 1.11 FPS for the G11, but the the A650 can only take four shots at a time while the G11 is only limited by the size of the memory card.
As randomlinh said, the lowered resolution on the same sensor is a very good thing since it should equate to improved picture quality, particularly in lower light situations.
The LCD on the G11 is .3 inch larger (not a big deal) but has 2.66 times as many pixels (a HUGE deal).
The G11 uses a rechargeable LiION battery which is a bonus for some people. I personally prefer cameras that use AA batteries so I can swap any time I want to, but not everyone agrees. This is the ONLY "downgrade" that I can find between the two cameras, and it's a matter of opinion rather than camera capability.
The G11 has an optical viewfinder that shows you what the camera is seeing (including zoom/framing). The A650 has a "tunnel" viewfinder which is truly optical but doesn't show the actual framing of the shot so you need to use the LCD to frame zoomed shots properly. Definite win for the G11 if you like to use a viewfinder.
The G11 weighs a whopping 55 grams more with its battery than the A650 does without batteries (the A650 weighs more with batteries - actual weight depends on the batteries), and the G11 is the same length, 10 mm taller, and 8 mm thinner (so it will actually fit better in a pocket).
edit: fixed a typo