In my experience, quality of construction / finish makes more difference than the material. Basswood is lighter than mahogany though.

Mahogany is supposed to offer greater warmth and sustain, but a basswood with a thru neck probably would as well. Basswood is also reputed to have a better low end response.

I've (right or wrong) never worried much about what a guitar is made out of - I own quite a few, of various woods, and each has it's own character and place in a tune (or not). I find pickup selection has more of an impact than chosen tone wood. The only exception to this was my decision to buy an ash telecaster rather than the usual alder body - I found the sound was slightly warmer...

If what you've got is a 'guitar A, or guitar B?' type situation, just play both.... and then buy both if you can :D you'll find a use for them I'm sure...