Broly's instance of vaporizing a galaxy is vague at the very best, we see it pix-elated away and then we see Goku travel there a bit later and it's in tact
Outside of that we saw Broly vaporize a planet but his durability sucks, against energy attack it's ok but against physical force it isn't, he had to use a shield to protect himself from lava
Telepathy might not work against him because of his rage but Thanos could potentially one shot him via energy blast or fist to the face
It depends how Thanos approaches the fight. He could very well have a new mind slave, but if he toys around, he could also be left floating in space since Broly's psychotic enough to dust the planet once he saw that he wasn't getting past Broly's shields. Thanos would work him in hand to hand also, but be at a disadvantage if he tried to blast it out with him. His best bet is to catch him with some high powered energy blasts or mental attacks before Broly goes all "KAKKAROT!!!!!!!1!" And starts pouring on the power. Broly's dangerous and its best to take someone who dusts planets with backhand blasts seriously. His durability is just against heat though.
Oh and lol @ Effect Veiler trying to lowball surfer by using a non canon comic that proves...nothing.
Thanos' durability is far beyond Broly's output. The guy never destroyed a galaxy. It was still completely in-tact, as the crew goes there and there are still countless stars in the sky on New Vegeta, it was simply being attacked, as was said in the narrative. That visual was simply representative of the future.
Broly is still faster however, as simply hitting someone with immense speed in comics does not mean your speed is on par with their own, not unless there is specific mention of it. Its a comic, speedsters get tagged all the time due to PIS/CIS etc. (And yes, make no mistake, Surfer is immensely faster than anyone in DBZ due to at least having a couple of a nanosecond level reaction feats--on such a scale, a full second would feel like a few decades. Literally. No one in DBZ has a perception speed anywhere near this fast, since 30 minutes is still considered a fairly short time for them via fusions.)
Broly's durability is immensely shit compared to Thanos, as being blasted into the sun was able to kill him for good, and that same blast did not remotely damage the sun despite the size of the explosion.
Broly's physical strength compared to Thanos is also such that an ant compares better to a top notch powerlifter than he does to Thanos. Literally.
Broly will eventually tire, as the ki fluctuations in his body takes a toll on him. Thanos can mindrape him or clothesline his head off when the opening presents itself.