If you choose the iPhone number, the text messages are sent out via your Phone and recipients saw your iPhone number. If you choose the watch number, the text messages are sent out via watch's own cell radio and will show up as your watch's number when received.
If you don't want to show your watch number in any case, you need to use NumberSync feature offered by AT&T. Once activated, your watch and phone will share the same phone number. However, not sure if it works with iPhone.