Karin for sure.

Tsunade is good, slightly overrated. When 6P Naruto gets skill trials, she might be more viable... however Karin heals much more, if you dont kill her with mystery storm, she heals everything up... and her mystery? You either manage to stop her somehow or her team plays with you entire round.

She is most versatile support available, get her... (you can get Tsuna in other events btw... but Karin is Tsuku only ninja so far.)

Because we got some diversity in opinions now, which is great. I will give you some real example which I recently had vs. both Karin and Tsunade while I used same team in both cases. Im using Kisamehada, Taka Suigetsu and Creation Kakuzu with Water main (also in this order based on positions - Kisame P1, Suigetsu P2 ...)
Im in 703k now, which I dont consider mid game anymore.

Vs. Tsunade (team consist of 10T Madara, GNW Madara, Fire Main and Tsunade)
1st round: I use all mysteries, enemy uses 10T Madara.. my team is dead except for Kisame, his team is at 40% except for 10T who is still at full HP.
2nd round: I get hit by 10T again, hit enemy with Kisame and kill fire main... my team ressurects. gets killed right after... at least my Kisame heals up...
3rd round: I get hit by 10T again, hit enemy again and kill his fire main and Tsunade, my team ressurects again... from this moment Tsunade cant do anything... even if she ressurects, she dies instantly. Fight goes on and whether I win or lose is based on my luck with evasion...

Vs. Karin (team consist of 10T Madara, Karin, Fire main and Nagato)
1st round: I interrupt Karin, get hit by Nagato and 10T...
in all other rounds it goes very similar to other fight... my team keeps dying and ressurecting... problem is, I cant kill Karin as easily as Tsunade.
In the end its same luck on evasion based combat where I either dodge and win or dont and lose...

Some comparison of them:
Both Tsunade and Karin heals for roughly 10k per heal.
Tsunade heals twice initially, Karin heals everytime you use mystery.

Tsunade cannot die for 1st 2 rounds.
Karin heals 2% HP per hit... (At my power, she has around 50k - 55k HP at P2 so 1000 - 1100 HP healed per hit)

Tsunade ressurects after you use few mysteries. But usually cannot use mystery if her enemy is counting, so she becomes pretty much useless.
Karin on the other hand deals poison and slow... which basically means, if you cant stop her, you will get interrupted later on. (P1 Karin is annoying)

Now to give you some math:
If you hit Karin with multiple hits (Kisame standard, Minato Standard / mystery etc) she heals multiple times...
If Kisame hits her with standard and deals 10 hits, she heals for 10k, (usually it just lowers total dmg done as Kisame deals more than 1000 dmg per hit)
however if you deal less dmg you are screwed (for example my P3 Kakuzu uses mystery on her). This mystery deals 5 hits, each hit deals 1700 dmg, she heals for 1000 HP per hit and I give her 3500 actual dmg... however she gets extra standard healing for 10k... so my Kakuzu helped Karin to heal.
Basically any mystery that deals less dmg than 11k will help her. Or to give some less specific formula for Karin...
Damage done by mystery must be higher than her heal + 2% of her total HP or you have to burst her before she starts to heal. Otherwise do not use mysteries... you will just help her.

From my experience, Karin is simply stronger as Tsunade helps you only in 1st 2 rounds.