Actually, 1/4" steel isn't all that stiff. Stiffness goes up with the cube of the thickness so a 3/4" plywood face would be about the same as 1/4" steel even though the modulus of steel is 210 GPa and plywood is about 8 GPa.It depends on a number of factors as to which method might be better. IF it's just stiffness you are looking for then bracing is the way to go.
If you "wrap" the exterior of the cabinet with MDF (1/2" to 3/4") with viscous glue (something that doesn't stiffen-up much), then you will likely be better-off than bracing (..and this is coming from someone that hates MDF) overall - irrespective of stiffness. Most people wind-up using bracing that doesn't raise the panel modes enough and then don't damp the rest of the panel (usually internally).
The best thing you can do (mechanically) is use a baffle that is ultra-stiff: as-in 1/4" steel plate (that the driver is mounted to) - which radically improves clarity. (..Impedance compensation/flattening Impedance also does this electrically). I would rate both as a much higher priority than cladding/bracing. IF it's a ported design I'd also *damp the port and wax/polish the interior of the port. Fiber-fill is best used wrapped-around dowel bracing and kept OFF of the interior surface of the cabinet. (..waxing the interior cabinet surface is also a good idea).
*with port design I'll typically use a larger pvc/plumbing pipe that surrounds the exterior of the vent pipe but with a small amount of space between them - and fill that space with softer pure silicone caulk. Basically a "pipe within a pipe" where only the internal one vents to the exterior of the cabinet.