honestly, I've never felt particularly impressed with a tile game using hexagons over squares. Its mildly interesting, but I have not seen a significant change in game play arise from it. I would choose the easiest route for development/design, unless you have a specific reason other wise, that brings good value to the game. Players don't tend to care about how you internally developed a game, and instead only care about what they see.
One thing I'm especially interested in is why people choose hextiles over triangles?
Is it just easier for the artists or is there another reason?
In my eyes triangles do have the same cons as triangles, however tringles can have at most three different neighbours which means the artists wouldn't have to make as many combinations as with hextiles.
First off, if you think about it, a single triangle only has 3 facing directions in your game, like you said, but your map will require at least 2 directions of the triangles, or a lot of unusable space. You'd still require all the same work only now there would be angle complications to figure out depending on which tile your on. where as with square or hex, you always have the same available exist angles and paths. - less to deal with code wise, and for mentially dealing with it. with triangle movements, you can not create a straight line unless its only 2 tiles. anything more and your lines must zigzag. In squares you have 4 directions you can make straight lines in, and hex you have 6. Easier on AI movement too.