Lemongrab is the most effective with his ability to catch enemies with his slow, AOE blind/silence is pretty hard to beat, and landing a double or triple dungeon will win the team fight. He is good at protecting teammates and also he has a great initiate and is able to protect himself pretty well in retreat. He is a bit weak in 1v1 to basically everyone, and he has long CD without the NUWW build, but with the NUWW build he has very poor damage all around.
Jake is probably my second favorite because he has a decent initiator with Q if you can land it. AP Jake does gobs of damage, and knockback becomes a powerful finisher. His passive combos well with his ult and Q. Jake is pretty slow and becomes a punching bag with no protection, and his damage early game is very poor. He has a lot of trouble clearing waves and jungling early game which makes it hard for him to level up and thus he falls behind easily. A behind Jake is pretty useless.
Fionna is alright as a tank I guess, she scales very well and is very tough to take out even with an aggressive build. The 6 seconds is very annoying especially to wizards who cannot dash, but ninjas can get out fast so they don't have anything to worry about. Her dash is not very fast, its just for catching people, but it is only a great initiator against single enemies. Fionna is super weak to any and all CC, which makes her a bit worse than the other ones, as Lemon can use his passive in coordination with enemy powers and Jake can break all effects by using his Ult.
Billy is pretty poor in my opinion, but that's just my take and I am sure some will disagree. He has amazing scaling in health, AD, and his PD and defenses are certainly acceptable. His weakness is in powers, which kinda suck a when it comes to being a good tank. His knockback is a terrible engage, knockback with stun is really only good as a defensive ability. His jump is just a worse dash and is very small AOE. Jump with attack speed boost is really only helpful for towers and jungle, as anyone you jump on will move and you have melee range so you have to walk to catch up and then in doing so you lose the attack speed. Also you cannot combo the stun with attack speed boost due to the way the passive works on every third power. Nothung is my least favorite power in the game, without the boost it just sucks. Small AOE for no time at all with an awkward targeting system. It just blows. With the passive if becomes a bit more workable, but keep in mind it is just like Jakes Ult but Jake can MOVE, and nothung just hits a small area. It is easy to dodge and would work better if you could stun then drop it, but the passive does not work like that. Billys main weakness as a tank comes from his inability to initiate fights and target select enemies and immobilize them so the damage builders can do the work. His powers seem a bit too clunky and his attack speed is very hard to work with at the melee range, but is partly make up for by his huge AD. I am sure some people are fantastic with Billy as a tank/fighter, but I would much rather have a Lemongrab or Jake on my team in the tank role.
My personal order of most effective tanks; Lemongrab, Jake, Fionna, Billy. What about LSP? She is ranged, and not really in the middle of the fight with her squishy bod. She has a bit of a different role, I think she heals her teammates early game and stays out of it, but late game she becomes a super beast and carries the team. She is technically a tank, but she has a different role than the others.