Tyrannosaurus vs. Azhdarchid

Azdarchid flies away, rendering the battle null
In all seriousness, if the Pterosaur was stupid enough to try and fight the Rex, it would probably die thanks to the possibility of T. rex simply biting the neck as the first attack. Vote goes to Tyrannosaurus here, though the beak would make a powerful weapon as said before.

Completely irrelevant

I highly doubt that. how light you are doesn't limit your capabilities in flight performance. no matter how light, a structure that's is aerodynamically built for flight would be capable of all the means of flight direction as long as the build is strong enough to withstand it. although being the most highly pneumatic animal that have ever lived, they retained advance honeycomb structures that keep it rigid and strong, just like birds. of course, it lacks the proper aerodynamic shape for high speed flight and definitely weren't for raptorial pursuit and where better at soaring and climbing. a controlled decent is a plausible ability and might even be necessary when trying to gain speed to achieve a higher elevation to catch thermals. it's a transaction as simple as elevating down. though, I doubt it's going a common practice for such pterosaurs.

don't get me wrong, your 100% correct on the notion of it not being able to dive at a predator. the results are a smashed pterosaur. i'm just saying that pterosaurs are capable of diving, which you however, stated vise versa. they can most certainly dive. just not for raptorial pursuit or fighting

Mismatch

T-rex wins this.