I think the context of
Deuteronomy 22:5 deals with cross dressing, and of course an off shoot of that may be to deliberately look distinct from one another. However, as has been pointed out, there were times in history when men and women wore similar styles, so I think the main idea is that we aren't to try to pass ourselves off as the opposite gender. (e.g., cross dressing)
As for Paul talking about modest dress, what he said was,
"...that women adorn themselves in modest apparel, with shamefacedness and sobriety; not with broided hair, or gold, or pearls, or costly array;" (
I Tim. 2:9)
According to Strong's, "
modest" means "
orderly, decorous,...of good behavior", and "
apparel" simply means "a
deposit; costume; apparel."
I don't know of any other reference to modest apparel in the NT. In Peter it talks about how our adornment shouldn't be "that outward adorning of plaiting the hair, ...of wearing of gold, or of putting on of apparel."
In THAT verse,
"apparel" means
"a dress, apparel, cloke, clothes, garment, raimant, robe, vesture." It's a pretty generic term, referring to nearly any type of garment. PLUS, you can't interpret that verse to be speaking against women braiding their hair and wearing gold, and then turn around and say that it shows they SHOULD be wearing dresses. (If you choose to narrowly interpret apparel as "dress.")