need help on what camera is better

Those two cameras are not intended to compete against one another.

The amount of optical zoom, physical size, and weight put them far apart.

Here is a comparison of specifications:

http://www.dpreview.com/reviews/compare_post.asp?method=sidebyside&cameras=canon_g11%2Ccanon_sx20is&show=all

The SX20 is Canon's top big zoom camera.
The G11 is Canon's premium camera.

The G11 is interesting this year because Canon finally broke away from the megapixel race.

The G10 had a whopping 14.7 megapixels which put way too many megapixels on a very small CCD sensor. That caused the need for even better noise removal in the firmware.

Apparently smarter heads prevailed and the G11 kept the same size CCD sensor assembly but only put 10 megapixels on that sensor assembly.
That should reduce noise because they could use larger pixels, which have greater light output.

From reports I have seen, the G11 buyers are loving the loss of all those megapixels.
The result is less noise and a much better performance in low light.

As far as competition in the big zoom cameras, here is a link:

http://www.dpreview.com/reviews/compare_post.asp?method=sidebyside&cameras=canon_sx20is%2Cpanasonic_dmcfz35%2Csony_dschx1&show=all

The Panasonic FZ35 and Sony HX1 are the competition for the Canon SX20.

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