Which Axe Cavalier?

if you want to decide between frederick and titania, go frederick, you already have 2 tanks so you dont need a third (Titania)
but cecilia would be the best green option for your team, she is a great brave lyn and reinhardt counter so there is no reason to not have her, then you could have a healer for your last slot (Since they got a buff) Elise is clearly the best healer as of right now, but you could go with another horse healer if you dont have her

Who's your 4th rider? Unless the answer is Reinhardt, who can take out any lance user with breaker and all but the most inflated of blue mages, I would strongly advise Frederick, just so that you have another character who's capable of nuking enemies out of existence.
If you do have Reinhardt, then Titania is a viable option if you're willing to go to that much investment - however, I'd personally still stick with Frederick, as Reinhardt is only one man, and such only gets one turn - you can't always rely on him to be able to clear the entire map.

...Or, as Afro stated - and I was too hung up on thinking about Axe's to contemplate, despite running her in my own team - the correct answer is run TAR Cecilia, if you want a third tank char.

Your other cavalry units have low or mediocre resistance so I would personally pick Titania over Frederick any time. Though she has better stats to focus on than defense which is not the best of her stats. She is kind of speedy unlike Xander and Berkut so it would balance out your team a bit. Speed and resistance are the only reasons why you would ever pick her over Freserick so you should definitely invest in her stronger points if you decide to use her. But then again, Frederick is a fantastic player phase unit with Brave axe. So he would be just as good for your team... Its your choice/preference really. Also depends on your 4th team member.

Titania is the only good green horse tank ATM. The others can have high def, but they will almost always be doubled.

I would recommend building both fred and titania, but fred will be a more offense oriented slot.

Titania is acutally a good choice, especially with a def+ IV.
The best IV´s for her are, def+/ -hp or res+/ -hp. The other stats of her are too important for a bane. She gets 5hp back with the refinement anyways.

Def+ would mean that her def is only 1 point less then her resistance. She gets 4 instead of 3 points, with 29 def and 30 res you could refine the slaying axe with res and give her distant counter. With ally Support and Fortify Cavalry she gets 37 def and 42 res.

With those stats you can easily kill Reinhardt, Cecilia or even Brave Lyn. Addtionally Iceberg would be nice. But you can also reifine it with def of course, having 41 def and 38 res is also nice, although i personally would prefer her res.

With +res she would get 45 res and 33 def in total or 41 res and 37 def with a def refinement. Those things are up to you, she really gets a nice amount of res and def, especially res can rise pretty good.

The great thing about her is that both stats have a good value and she also has a good amount of spd too. So she doesnt get doubled unlike Frederick who doesnt have much res and gets more often doubled.

Frederick is good for attacking or for tanking physical hits, whereas Titania can be more versatile, her stats are just more balanced which is convenient for different situations.