Eye relief was always my top criteria (so I can keep my glasses on). Essentially all low-end binocs have way-too-short eye relief. If a manufacturer goes to the trouble of using high quality eyepieces with good eye relief (18mm or so), then the rest of the device is probably well designed.
I've had 10x and higher, but can't hold them steady without bracing my arms, so I stick to around 7x these days. For me, 10x and higher needs a tripod, so they're not very portable.
I used to worry about exit pupil for astronomy use, when I was young and a 7mm exit pupil was appropriate. Our eyes don't dilate as much as we age, so now 4mm or 5mm would be fine, but 7mm would just waste light. Not that I, or perhaps you, use them for astronomy any longer.
Anti-reflection coatings are a good thing, but don't go for the gimmicky ruby or other exotic colors, which are useless and maybe even detrimental. That's just sales pitch junk.
