In principle there are three types of glues used here in pen turning.
Epoxy, Polyurethane (Gorilla Glue) and Cyanoacrylate (CA) glues.
As with so many things in life, different people have different preferences. I will tell you mine.
For gluing in the tubes in all types of woods and burls and all my stabilized (BB) blanks, I use polyurethane, i.e. Gorilla or Titebond.
Reason is that these glues foam and expand a bit and fill gaps and voids very nicely (example is that I drill all my flat top pen blanks with a "P" instead of an "O" drill bit, which can be sometimes a bit tight). In the past I used Gorilla glue, but switched to Titebond (half the price of Gorilla, a bit thinner and spreads better and also sets faster, although the created foam is not as dense as Gorilla's). I make a lot of pens during a year and had not one so far fail because of the glue (like tubes coming loose). Sometimes the foaming effect can push a tube out a bit, but this maybe happens in one of 30 pens or so. For me the use of PU glue makes sense since I always make at least a batch of 10-20 pens at a time (cut, drill and glue in the tubes one night and start turning the next evening).
CA I use sometimes for finishing pens, but must say that I am not really happy with the reproducebility, some times it works fine, the next time not. Ca is also used for gluing in tubes in acrylic blanks.
The glue is colorless and does not discolor my painted brass tubes (one must color the brass tubes for acrylics, if not the brass will shine through on the lighter colors), and it seem to bond well with the acrylic material.
Epoxy glue I use for gluing in tubes in metal pens (Aluminum and Titanium), and the reason here is that the glue is a bit more flexible than CA and PU needs humidity for a good cure.
Was a bit long, but I hope it helps you making your decision on what glue to use.
Rudy