The DA has a higher aspect ratio than the Cessna hence it is more sensitive to gusts and turbulence. The low wing makes the DA float for a very long time over the runway in summers. Prop and tail clearance is lower in he DA. Hence it is more prone to prop or prop strikes.
On the plus side, I find the DA's cockpit more comfortable than the Cessna.
(P.S. I am using the DA 40 for comparison)
But this is just for your information, And as someone above said, You should be looking more at the quality of flight school than the aircraft.
Cheers and all the best