There are some structural differences to gluing the extension. Whether they are advantages is up for debate.
You gain some lateral stability in the neck but when I was making prototypes for my raised fb design, I did some very scientific testing.
I held on to the guitar body with one hand and gave the nut end of the neck a couple dozen
hard blows from all directions with the other hand. I also leaned it against the wall and knocked it over a few times. No problems whatsoever. That was with a small (but reinforced) heel with a butt joint and 2 bolts.
You also spread some of the neck load to the top when you glue the extension. The string tension is pulling up on the neck which wants to rotate the top of the heel toward the butt and the fingerboard down. Gluing the extension to the top spreads some of that torque to the top in a different way that an unglued extension. The extension spreads that downward force to the top and onto the upper transverse brace and toward the rims. The top and tranverse brace then provides some structural resistence to that force as well as adding mass and stiffness to the fingerboard extension which keeps you from losing energy when you play fretted notes over the body.
With a floating extension, you have to account for the loss of that structure. I add carbon fiber rods from the heel block to the waist to resist the torque. To keep the frets over the body stiff, I continue a thin extension of the neck wood under the fb extension and reinforce it with carbon fiber bars. (by the way, I didn't innovate any of this and don't really know who to credit because I've seen various aspects of it in many places)
As for sound, there's no A/B comparing them. If you built a traditionally braced guitar and just didn't glue down the extension, I think you would lose something (and it just wouldn't make a lot of sense). Connecting the extension to the top does help the sound, from what I've seen. But with a floating fb, you can eliminate the transverse brace and in genereal, I find that I can get a lot more activity in the top in the upper bout than with traditional bracing. But they are different beasts and I wouldn't say one is inherently better or worse.