Okay, let’s have a look at this. I watched a lot of the recent tournaments and I am also playing on a fairly high level (18xx) myself, so I think I should be able to judge this somewhat well. Let’s use 5 categories:
5 - UU is basically part of every gameplan and absolutely crucial for that civ
4 - UU is a very good option and seen very regularly
3 - UU is a decent situational option
2 - UU is a niche unit, which is rarely seen, but still appears sometimes
1 - UU is basically useless and never seen, except for a few extraordinary games
Note: This is about games where players are actually trying to win, not about Viper having fun in ranked games.
I also wrote in brackets in which direction this unit is going: 4 - Camel Archer (3) means Camel Archers are put in 4, but are closer to 3 than they are to 5. If there is no bracket, I think the unit is right where it should be 
5 - Arambai, Huskarl, Mangudai, Conquistador, Longboat (4)
4 - Camel Archer (3), Konnik, Woad Raider (3), Cho Ko Nu, Kipchak, War Wagon, Magyar Huszar, Plumed Archer, Caravel, Sergeant (3), Rattan Archer, Berserk
3 - Jaguar Warrior (2), Cataphract, Throwing Axeman, Tarkan (2), Kamayuk, Slinger, Genoese Crossbowman, Condottiero, Samurai (2), Organ Gun, Keshik (4), Janissary
2 - Genitor (1), Longbowman (3), Coustillier (never saw this in a tournament, but small sample size and I think it has potential → 3), Shotel Warrior, Leitis, Karambit Warrior (will get buffed though and then probably be 3), Gbeto (1), Teutonic Knight (1)
1 - Elephant Archer, Ballista Elephant (that one’s a bit tricky. It is used for wood cutting in Castle Age, but not as an actual fighting unit), War Elephant (decent for ultra lategame in teamgames, but it basically never gets there), Mameluke, Boyar (2, the rating is probably more because Slavs have very good other options, because the unit itself is actually quite decent)
I left out Imperial Camel and Imperial Skirmisher, as they’re unique upgrades to existing units, not unique units themselfes (they’d both be ranked pretty high though).
Overall I’d say only categories 5 and 1 are problematic - then again I think even 5 is good, as long as it’s only a few civs which are that reliant on their UU - so I think that’s actually a good thing. So only the units in 1 are a problem, because they’re basically non existent (note though, that most of them have a comment in brackets behind them…).
So we have in numbers:
5 - 5 units
4 - 12 units
3 - 13 units
2 - 8 units
1 - 5 units
Looks pretty good to me. I might be off a bit with some of them, but I don’t think more than 1 position and the overall picture shouldn’t change.