Ratty, it's pretty simple:
1. Kodak has Tri-X, which I know better and like better overall than any other film (though I'm sure I could get along with HP5+ just fine, I like what Tri-X in Diafine does when I need speed but not quite TM...er, Delta 3200 speed.
2. Kodak has TMX and TMY-2. Fuji Acros competes with but is different from TMX. More important is TMY-2. Fuji has nothing (right now) in that speed range in black and white. Ilford is the natural competition in B&W, not Fuji. If they'd start making Delta 400 in sheets again I'd almost certainly switch for my 4x5. But they don't, so I haven't.
3. Kodak has superb color negative films unrivaled by anything available from Fuji. As far as I've found none of the Fuji 160 variants are available in the US any more, Reala is ok but no Portra, Fuji 400H looks like a film from decades ago (which may be ok when that's what you want but doesn't compare to Portra 400) and they have nothing even remotely comparable to Ektar. Further, the films they have that are available in this country, Reala and 400H, are not available in sheets.
Fuji has one (excellent) medium speed black and white film in 120 - the promised return of Neopan 400 hasn't appeared yet - and Velvia and Provia in a couple of variants each. They are excellent films, but they are not competitive with TMY, TXT, TXP, Portra or Ektar.
If you want color transparency Fuji has you covered, which is good since they're the only game in town. Likewise if you want a medium speed black and white film with unusual "orthopanchromatic" color response and the least reciprocity failure around, virtually none at usual exposures. But otherwise, they just don't have the products.