I would say english first. It helps you feel the horse better and teache them how to respond to you on a contact. Then you can start letting the reins out. It also depends on the horse and the trainer et cetera.
I think I would prefer teaching a horse western first. If nothing else than for the saddle. It is much easier for me to ride a young or spooky horse in a western saddle. Especially if they decide to buck. I also think it is easier to teach a horse to start collecting on the bit from a loose rein than go to a loose rein from constant collection. But that may just be me.
English, get a better foundation.... You don't have to start off with contact to start a horse off English. Starting English you first have to get the horse moving from behind then once you master that is when you start asking the horse to accept contact and more collection. That's just my opinion.
I would personally say that it's better to teach a horse english first because english is much closer contact than western which can be very helpful in keeping your aids clear. The key to english is not extreme contact with the mouth, you can keep your horse on as loose of a rein as western if you feel it necessary. The key is teaching your horse to move from behing, balance, and to hold himself up. I've found that once your horse is trained in english it is very easy to switch to western, but it also depends on the horse.