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The Presta valve is better when the rim is very narrow. The thicker Shraeder stem requires a bigger hole in the rim, and the thick rubber pad at the base of a typical Shraeder tube's valve stem is barely accomodated between the tire's beads.

Presta valves more easily separate from the tube, but Shraeder valves sometimes get a pressurized blister in the rubber coating, leading to rapid air loss.

A pocket-type air pump can have a lighter attachment head with Presta, no need for a valve-depressing plunger or the bulk to accomodate any moving parts.
The Presta valve stem appears to be lighter and more aerodynamic.

Shraeder valves require a cap to keep dirt from settling in the stem, which gets blown into the pump head as soon as the leverlock is actuated. This can foul the mechanism on some pump heads.

For racing bikes, Presta gets the nod. But for most others, Shraeder is easier overall.
Presta is the standard for road bikes, and certain pocket pumps are dedicated Presta-only.

Lastly, very narrow Shraeder tubes end up with the thick pad wrapping at least half-way around the tube, which confines all of the tube's elastic expansion to the strip of thin rubber opposite the thicker rubber pad. This can more readily lead to rupture if the tube is used in a larger tire.

I believe that Presta valves (more specifically their attachment to the tube) would prove more durable if users only knew that their Presta pump head is only supposed to by fitted to the narrow tip of the valve stem. This would greatly reduce the forces that typically lead to failure.