Gibson used to use Brazilian rosewood until importation of that wood was banned.
Importation of Brazilian Rosewood was banned in 1992 until CITES (some exceptions to be discussed). It was and is considered the king of tonewoods for acoustic guitars, both because of its tonal qualities and the wonderful chocolate brown color with great swirling grain. All of those $200,000 -$500,000+ pre-war Martin D-28s that are considered the Stradivarius of acoustic guitars are Brazilian Rosewood with Adirondack Spruce tops (with forward-shifted bracing).

Again, although Gibson used some Brazilian Rosewood, Gibson's always been more into maple and mahogany acoustic guitars.

It's still possible to get Brazilian (lower-quality Brazilian) at a high price, but the luthier has to have a lot of paperwork showing that the wood came from a tree cut down before 1992. That era of getting Brazilian from old stumps is an era that's pretty well passed, however.

Madagascar Rosewood was illegal to import (under Madagascar rules, I believe) for years, but a coup made it possible to get some into the country over the last decade or so. It's the closest thing, tonally and in looks, to Brazilian that we've seen.

East Indian is nice, but nothing like Madagascar or Brazilian Rosewood.

All of that is said with respect to using the wood as a tonewood, and not just as a fretboard or the veneer on a headstock.

And using Franklin Titebond instead of hide glue makes a difference, I believe. Think of pulling away old white glue. It still has a rubbery feel to it. Hide glue is brittle. When you want to transfer vibration from one wood component to another, rubbery white glue, no matter how well cured and now matter how thin the coat, dampens the vibration. That's what I hear from luthiers and based on guitars I have that are made with hide glue, I believe I can hear the difference.

Not to get technical but C.F. Martin Guitars are not a competitor of Gibson guitars.
C.F. Martin makes acoustic guitars exclusively. Gibson does not, they mainly make Electric Guitars. From the famous Les Paul model to the popular 'SG' model, the 'Flying Vee', and the semi-hollow body ES-335 'Dot', and like BB King's ES-345 'Lucille'.

The competitor for Gibson is Fender Guitars and their Stratocaster and Telecaster models. Many famous players like Eric Clapton start out with the Gibson Les Paul then switch to the Fender 'Strat' for the different sound a Strat makes. (Clapton's Fender Strat 'Blackie' sold at an auction at Christie's in London for a whopping $959,000!)