I chose European though it was really tough to decide. There are so many ways to change up a simple European weave and it can be used to wrap items, made into guitar straps, etc. And, let's face it....it is pretty darned handy for armour!
I went Euro.. mostly because its my good ol' standby. I recently sat down with the vague mission of making a dice bag for a friend and had only my random stock to do it in. The bag ended up being Euro 6in1 sides, 8in1 bottom, 4in1 gussets, and a 2in2 neck. And it has square corners... because cornering Euro is apparently my secret love. My secret, crazy love.
I chose other... not because I have another style I like, but because I can't pick a favorite yet. I want to try it all. So far, I have made my own patterns, made some dragon scale, and Full Persian. I have done some 4 in 1 and a few other little trials, but so far all I really do is look at the books and patterns online and drool.
Euro. (Although my ultimate fav will always be Dragon Scale, I don't know what family that is!) I love the ability to create pictures and designs with it. It's also easy and fast and progresses quickly. (Meaning you can actually see the work grow as you go.)
I chose European because I absolutely LOVE elfweave! I like combining weaves, though, like incorporating a Persian edging to a European cuff, and have been thinking of combining helm with some other families...
In all honesty, I like making it more then I like making most other weaves, and I did help a bit with that curtain project from TRL a few months ago (did around 40K rings) and it was all E4-1 and it got pretty boring in the end. I will admit, I like all weaves too, but I say again, Persian seems to be my favourite.