.357 Mag

Pros:

-More versatile (shoots both .357 and 38 spcl)
-More powerful (when shooting .357 mag)
-More robust (has to handle higher pressures)

Cons:
-In identical models, sometimes a bit heavier.
-Harder to control (if using .357 Mag)
-More expensive (in general)
-Not a great return on investment performance wise over the .38 special.

.38 Special

Pros:
-can be lighter
-less recoil = more control, less flinch factor
-less expensive.
-adequate personal defense round with proper bullet selection.

Cons:
-Cannot shoot .357 mag