Well actually you looking at two very different notebooks, for starters the G551 is a 15" notebook the G751 is a 17" notebook very big difference.
Actual I have been using my G75 for 3 years now with the battery in and plugged in. The Battery still last a couple of hour when I forget to turn on the UPS its plugged into. These new batteries and notebooks are set up not to destroy your battery with out you doing anything. Since you don't use the battery and most likely work quite a bit as I do. Setting up for weeks at a time in maybe different locations. But Still a desktop replacement I think you should go for the G751 larger screen and as you say better cooling. If your not carrying the notebook around every day you'll enjoy the extra size of notebook. If you do have to carry this back and forty often daily you might want the smaller size and screen. I think mostly students and business people that travel a lot go more for the 15" model. IMHO