Very interesting topic! I'm interested in this myself.
Never had experience with a trans girl... but I'd assume that two trans people dating must really get what the other one is going through. And yes I do think trans people in general understand both sexes to an extent. Just bcos of all the ->-bleeped-<- we've been through. At least for me I've become very sensitive to injustice and sexism in general. Having felt prejudice, exclusion, social isolation, sexism, pressure to be something you're not, pressure to conform etc. etc. you don't necessarily wanna treat other people like that...! I wouldn't push gender roles on children, I would never think 'girls can't do something' or 'boys can't be like that' etc.
Though really understanding the other sex thoroughly because you were forced to be that - don't think so. I still get guys more than girls in general. Just bcos the society tried to pressure me into being something I'm not doesn't make me understand that any better.
And as for dating... I'm in a beautiful, lifelong relationship with a cis woman. She has always supported me 10000000% and there has never been things between us she wouldn't 'get' bcos I'm trans! She's a person - I'm a person - we are a couple... It doesn't matter if I'm trans! If she were trans too (and had a dick for example) it wouldn't change anything. I don't think trans women are any different to cis counterparts and vice versa. It's all about the people in it.
I'm interested to know what you think trans women can offer you that cis women cannot? Thinking about sex the first thing to come to my mind is that many trans women hate their genitals and don't like having sex before SRS...
Plus generally speaking two trans people in a relationship might be double trouble/dysphoria. Though there are many trans couples. I really don't think it matters if someone is trans or not! It's all about the chemistry.
And as for understanding identity - as a pre-everything (and being like that forever!!!) I can totally say my spouse understands my identity

! And always has, so...! If she didn't, we wouldn't be a couple. Just saying that cis people can be exactly as accepting/understanding as trans people

. Again - chemistry! And I don't definitely view myself as somehow 'flawed' bcos of being trans! It's not my fault I was born this way - and I don't need to be pitied bcos of it. Or treated any different than any other guy. We are a couple because we love each other and get perfectly along. Gender does not play a part.
She's also completely straight

!!! And still she's with me bcos she just sees me as a guy, so.