I think when you are purchasing a laptop it is important to buy one with a good history of reliability and customer support. I personally would never buy a Compaq, and I don't know much about the Averatec. PC World publishes a reliability and service support report each year. This years has yet to come out, but you can find last years report at
PC World Reliability and Support Report
Of course PC World's information is aggregated data, and personal experiences vary, but I personally would want to maximize my chances of getting a laptop that lasts, and that if something did happen, it would get taken care of correctly and in a timely manner. Dells, Apples, and IBMs tend to do well on these reports year after year. I know that they cost more, but it may be worth it in the long run.
Your real question probably had to do with what computer specs to go with, and it depends on what you want to do with the computer.
Here is how I see it
Compaq - I see this computer mainly functioning for checking email, posting on TFP, and writing papers. The M processor simply means that its a Celeron "Mobile". Supposedly these processors use less battery power, and allow the computer to be lighter.
Pros
512 Ram
Wireless G included
DVD CDR Combo
60 Gig Memory
Fairly Light
Cons
Celeron Processor
Shared Graphics Card
Smaller Screen (You may like the smaller screen though)
Averatec - This is a much faster computer that would be more responsive, it also has a DVD burner which is nice. It has a nice screen which would be nice for watching DVD movies.
Pros
Relatively Fast Processor
512 RAM
60 Gig Hard Drive
DVD Burner
Good Software Package
Wireless G
Big Screen (15.4)
Cons
Heavier
Integrated Video Card
Doesn't specify what the battery actually is
This is just my opinion of course, and I hope you find this information helpful