Another possibility is death metal. 1991 or so is when some death metal bands started getting mainstream attention - bands like Death, Cancer, Obituary, Carcass were all starting to be looked at by the major labels. Death metal is not intristically the easiest style of music to sell to the masses, but then, who would have thought that grunge would get as far as it has?
Funk-metal movement was a non-starter around the time - a short lived craze that failed to generate much more than early hype. At the same time, bands like Korn are starting to get popular by mid-90s, and since Ministry, Pitchshifter, and Depeche Mode already have made their mark, industrial/industrial metal can still be popular.
In reality, grunge scene only had about 5 years of life in it - by 1996 it was overtaken by rap metal and nu-metal crowds on one side, and goth/industrial rock on the other. In other words, in 1996 more new bands tried to be the next Korn, Limp Bizkit, or Marylin Manson than the next Nirvana. Honestly, I see some of the same trends in music as in OTL in the US, except that we might be spared the horrible, horrible bands like Creed, Godsmack, and those that sound like them.