I like PA but I'm a little biased as I am one of the Assoc editors and do quite a bit of writing for them. It covers stuff that I am most interested in, hunts I could actually make, build alongs and covers some history too.
The Bowyers Journal is a new magazine to the market (just over a year old) which covers wood and glass bows, hunts I could actually make and build alongs as well. I like it alot and do some writing for them as well. Lots of Tradgangers contribute to TBJ.
TBM while being a fine magazine and the "slickest" of the three, usually covers glass bows (although they are starting to cover wood bows), usually are about hunts I'll never be able to make (but enjoy reading about).Don't do much in the way of build alongs (that I recall) but do cover some history from time to time.
I have been as subscriber to all three since they started (as well as the now defunt Instinctive Archer which I really enjoyed as well)