How big of a frag tank? I'd go with the cheapest option. Simply put frag tank you might not have fish in it, or VERY limited fish (perhaps a wrasse or something to deal with pests), I probably wouldn't bother with feeding the corals much either (unless you are interesting in growing out corals galore outside of your main tank.
I think both of those skimmers you listed can handled 200g of good sized fish load fairly easily,and AFAIK the BM is WAY cheaper then the BK skimmers which IMO doesn't have that much extra stuff to justify the cost difference.