Yes. There is a difference between basswood and mahogany. They type of mahogany can also be a difference. There are also many other factors as well. Maybe do a little research on the woods as well as Google. The Suhr site used to have an excellent breakdown of how the different woods sounded with relation to guitars.
But generally speaking, basswood is totally balanced/flat. In many instances, it is chosen for being light weight. It's pretty soft.
Mahogany is generally a little richer and fuller sounding. Some people consider it to be bass-y, but I've only experience that with a mahogany body that has a mahogany neck. Maple necks can balance it out, as well as the quality of the mahogany (cheap wood doesn't always sound as good as a better selection that might cost more...it just depends).
I don't see a huge concern over mahogany being really bassy and tubby in an application like this. A difference? Sure. But most people find that although you can add girth to a bright guitar, you cannot remove the low end from a guitar with a pickup selection. Just find something that accentuates what you are working with.
Be judicious when listening to sound clips to factor in that players style, whatever amp they are using, the recording conditions, and any effects being used that might distract from the real pickup tone.
For starters, what is it about the pickups in there now that you want more or less of?
