I always thought of it this way:
Gandalf knows that in a contest of wills between Saruman and Sauron, Sauron won. He has no reason to believe he's that much stronger than Saruman. That answers the question as asked.
However consider the risks.
Sauron is no fool. He knows who Gandalf is, and possibly his greatest fear is that Gandalf will claim the ring for himself (it never occurs to Sauron that the council would try to destroy the ring, for him it was a question of who would claim the ring first). He knows that Gandalf, of all people, probably knows where the ring is.
Let's say Gandalf picks up the palantir for a bit of banter with Sauron. Sauron will immediately see that Gandalf isn't wielding the One Ring, and he will bend every bit of mental muscle he has to wrinkle its location out of Gandalf's head. He'd see the actual plan (hobbit to throw ring in Mount Doom), he'll see the battle before the gates as the diversion it is. Any hope for Middle Earth is extinguished.
Sauron also learns that Gandalf carries one of the three, and will learn also that Galadriel & Elrond also carry rings, compromising those two and their realms.
So the single greatest asset the good guys have (Gandalf) is compromised, as are their only allies.
The risks for Gandalf using the palantir are astronomical, but to what end? What will Gandalf learn that's worth the risk?
Aragon is the safer choice, going for shock and awe, the bloodline & the blade that slew Sauron's corporeal form and diminished his spirit. There were still risks, but as you say, they are mitigated by Aragon's innate right as master of the palantir.
Also consider that Gandalf (like the other Istari) is forbidden from tackling or confronting Sauron directly, he can only help (direct and encourage) others in their struggles against the dark lord.