Amoonguss
Pros:
It resists the STABs of very common Pokémon in OU with its great defensive typing, allowing it to play a great defensive role with its high HP.
It is a poison type, meaning it can use Black Sludge.
It’s much more well rounded with its bulk, and it can utilize Black Sludge while Tangrowth is stuck with an Assault Vest due to its bad Special Defense.
The most important thing, in my opinion, it gets Spore, the only 100% accurate sleep move.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Cons:
It doesn’t have great offensive or defensive stats, and even if it’s more balanced than Tangrowth, it won’t be able to tank/wall as well, in my opinion.
It’s in UU for a reason, while Tangrowth is in OU.
Anything faster with a super effective move could easily get the KO if it has a high Attack/Special Attack stat (252 SpA Choice Specs Tapu Lele Psyshock vs. 248 HP / 56 Def Amoonguss in Psychic Terrain: 728-860 (168.9 - 199.5%) -- guaranteed OHKO, I used preset movesets for this calculation).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tangrowth
Pros:
It’s in OU. That’s always a good sign when playing OU.
It has great HP, Defense, Attack, and Special Attack, and it can reliably run an Assault Vest set with no offensive EVs and still hit hard.
It gets Knock Off, allowing it to cripple item reliant Pokémon.
It has a good movepool, and it can combat it’s weakness with moves like Earthquake and Hidden Power Ice, and it gets additional coverage in Sludge Bomb.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Cons:
It has horrible Special Defense and relies on an Assault Vest to patch it up, which hinders its walling capabilities, though it does make a good tank.
It has a worse defensive typing, and it can’t do much about Fairies with Hidden Power Fire (while Amoonguss usually scares them away due to a STAB Sludge Bomb).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I think they’re pretty even, actually, both having a fair amount of pros and cons.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope this helps! :)