Farming servant

I recommend you take a look at the page called "Strongest NP" on the left side of the screen, under Tools. It appears that Fran deals more damage than Tamamo Cat.
I can't say for sure that one is better than the other, you'll need to take a look at their skills, and determine that yourself.
Also Fran is just too adorable, maybe some bias there.

Having both is definitely nice for farming. In my experience, Fran generates higher damage values, which is typically more valuable in a berserker but that won't matter on dailies.

Frans deal more damage, she has a def down skill and an NP damage up skill.
Tamacat only has a single atk up skill.

To put it more ''complex way '' :

Tamamo Cat - only has Atk Up, lesser base NP damage. You need NP Up + Quick Up to fight Fran NP total damage but it's still won't do, because Frans has higher base NP damage. Don't forget adding a def down Debuff will make it even difficult.

Frankenstein - Def down, NP Up, higher base NP damage. She totally wins if you can give her a Golden Sumo CEs or any CEs that increase Atk or Quick card performance.
Don't forget about damage multiplier here, same buff only stacks additively but different buffs stacks multiplicatively.

Both is good for farming, you only can use them once since their self stun demerit is so annoying. Unless you can remove the self stun debuff, but it's not really recommended.

Bonus : i have both and they're pretty much like a ''twins'' gameplay wise. Raising their Bond level and raising both of them can ease your farming activity. Put some Battery CEs like Golden Sumo, HNS, Kaleidoscope, Halloween Princess, Imaginary Element or any Battery CEs then you can clear almost any High HP enemy waves especially for farming multiple event bosses.

Imagine if we have Skadi or simply just use Helena with a Kaleidoscope, Frans base atk + Atk Up * ( Def down + Def down ) * NP Up * Quick Up ( Skadi/Helena Buffs ) = all buffs stacks multiplicatively and you can destroy almost everything with NP 2 Frans but only a single times because of self stun demerit.
Backliner supp not even come out to give Frans greater buff, imagine how easy it is to clear lvl 80-90++ event quest with multiple enemies using NP 2 Frans and the right set up.

Great power comes great responsibilities, Frans damage maybe high but every servants has it's own weakness ( annoying self stun LOL and Zerker take double damage ), no exceptions.

I don't mean to offend people and sorry for the longpost.

I’d probably go with Fran out of the two if your only gonna be picking one. Fran can increase her own NP damage and her Defense down allows everyone on her team to hit the target a bit harder plus it has a chance to stun. Tama cat only has a self attack increase to improve her damage so she won’t be hitting as hard. So yeah if your just gonna pick one for now I’d start with Fran, both can used perfectly fine for dailies but Fran being able to hit harder will be more handy outside of dailies where mobs might have a bit more health.

Fran.

But you will eventually want to retire her in favor of TamCat/another Ape berserker once she hits max bond