i personally like rosewood.
What material would be better for a chess set?

Some rosewood is very grainy and there are players who feel that lack of uniformity detracts from the look of the set. Others love the look. Ebonized boxwood is certainly a "safer" choice, but it's pretty much your call as to what you think your coach would like.
The white pieces are almost always boxwood, so I guess that you are talking about the black pieces made from rosewood or ebonized boxwood respectively. A matter of taste. Ebonized boxwood is deeply black, while rosewood has a very inhomogenous structure.
See http://www.regencychess.co.uk/chess_woods_guide.html?zenid=ne2412h43pa42tuio1s50816f3

for me, i'm not a big fan of the "big grain" look that rosewood usually shows ... that's just my personal taste but your coach may like that ... does he have some other wooden sets that might give you a hint at what he prefers?
for my taste, ebonized rosewood is very good ... tho if you want a more 'wood-like' appearance, i think an 'antiqued' Sheesham, a finish technique that gives the look of a nice patina without the big grain :) -- an example of that look is available here:

If the two sets are the same price the ebonized boxood set is presumably superior in some way, since rosewood is the more expensive material.
If that is so, I'd go for the better designed/finished set.
A clunky design in rosewood, or one with a somewhat rough finish, isn't all that attractive to me.

I'm thinking about buying a wooden chess set as a gift for my coach. There is one made of boxwood and one made of rosewood.Both are $200. Which is better?
Rosewood is better, but you need to clean it with a high quaility wood polish. Rosewood is prone to soaking up skin oils. Unless of course it is clear coated with urethane.
I'm thinking about buying a wooden chess set as a gift for my coach. There is one made of boxwood and one made of rosewood.Both are $200. Which is better?