Basswood vs Mahogany
I'm not a luthier or anything, but I've been playing for a long time and have owned tons of different guitars, and I think I may be able to give a little input here. *Keep in mind that this is only opinion, and there are many, many variables involved such as pickups, neck scale, type of bridge, etc....
My personal feeling is that basswood sounds, well.....I think the word is "tighter". *It seems to resonate quite well, and I have been told that this is because it is a rather open-grained wood. *I think it has more high-end (treble) qualities than mahogony.
Mahogony, on the other hand, sounds to me like it's "fatter". *It's tighter grain and greater weight seems to harken to the low-end and give it a nice classic-style "punch". *Once again, this is opinion. *But if you examine one of the most classic rock guitars ever built, the Les Paul, the body is mahogony topped with maple. *I have been told that the maple is there to add a crisp, high-end tone.
Once again, only opinions. *I'm sure there are many more folks out there who could add much more to the subject, and I sure hope they do.
The best advice is to go out and play them. *I would sit down, dial in the amplifier, and not touch it. *Maybe even set up an "a/b" pedal so you can switch guitars quickly and not loose the ear for the previous tone.
Once again, keep in mind the variables. *Pickups, string guage, neck wood, amplifier, even different sizes and guages of picks can affect tone, at least to some extent.
Good luck picking one!!