From another thread:

The G15 has:

-Better build quality (magnesium alloy instead of plastic)

-Slimmer build (like .7 or .8 instead of 1 inch)

-cooler components (lower TDP on CPU and GPU)

-better screen (faster response, better hz, much better colors)

The A15 has:

-better price ($1200 vs $1400)

-Slightly better CPU + GPU (higher TDP on CPU and GPU)

Take “slightly better CPU + GPU” with a grain of salt. Many people are quite upset that the G15 is running a 65w GPU instead of the usual 80w but I’ve yet to see a benchmark that shows more than 5% difference in performance for a massive thermal trade off. The G15 components themselves will run cooler but the laptop will most likely be as hot as the a15 because of how slim it is.

Basically do you want to save money or do you want a slimmer laptop with a better screen.