The Boba Fett and Captain Phasma conversation

In the case of a connection, most likely not. I have just read the Phasma book and there was absolutely nothing to indicate contact of any kind, and the book is based entirely upon Phasma's origins. She really is kind of the Boba Fett of the trilogy (though nowhere near as cool) but I don't think that indicates or was meant to indicate a connection of any sort. Most likely, she WAS intended to be the Fett of the trilogy, but probably just to give that same sort of character to the movies. As for who would win in a fight, Phasma is a brutal warrior, ready to sacrifice anything and everything to win. She is extremely talented, and obviously not one to be taken lightly, but neither is Fett. I believe Phasma is simply too overconfident, and almost too desperate to win. Fett is much more calculating, observant, experienced, and intelligent, than Phasma. Because he talks so little, everyone pays attention when he does speak, and part of Fett's gift as a bounty hunter is his ability to push all the right buttons. He would be able to identify her agenda (for she does indeed have one, but I won't spoil it for those of you who haven't read the book), and use it against her very early on. When people get mad, they get careless, Fett knows this and often exploits it, and I believe this would be her downfall. In addition, Fett can fight with any and every weapon in existence, so while I think Phasma would still be able to put up a MUCH better fight than most, I think she would still lose. And Fett would win. Every time. (Please note: I did my very best to be unbiased lol)

Honestly, If there was a Battle between Boba Fett and Phasma, Boba would win.

I’ll put it like this:
Finn loses a battle to TR-8R (A NORMAL STORM TROOPER). Then he goes into that Hibernation tube when he fought Kylo Ren. Which means Finn had no proper training when fighting Captain Phasma. AND FINN WON! Meaning Captain Phasma has less skill then a basic Storm Trooper.

So yeah...Boba Wins