I have looked up both the datasheets of ATmega8 (not ATmega88) and ATmega168 and upon comparing the features listed in the first page of the datasheet and the pin out diagrams, I could see following differences:

(1) Amount of Flash memory

(2) Interrupt and Wake-up on Pin Change

The rest looks like pin to pin compatible. I am not sure how to compare 2 different micro controllers functionally without reading through 400 pages. Which pages should I be comparing to get to know the significant differences between the controllers (from a enthusiast point of view)?

BUMP

I would also like to know the answer to this question; I would be interested in knowing how to compare differences in these components as well!

This might help a bit:

www.nerdkits.com/forum/thread/215/

The front page of the datasheet is definitely going to give you most of the information you are looking for, or at least provide a good enough overview of the chip that you can tell what the major differences are. Other than the memory, and a few interrupt differences the biggest difference I see in these chips is the max clock speed, which is slower on the smaller ATmega8. Definitely check out the thread that Nerdful pointed out, as there are bootloader issues that you might need to think about too.

Humberto