Then your 12" dob has some pretty crappy optics. There's absolutely no optical reason why a low f/ratio reflecting telescope will perform more poorly than an equivalent diameter longer focal length scope. Yes, you may require the use of a Paracorr II to minimise coma, but that doesn't affect the area subtended by a planet's surface in the eyepiece. If you have a short focal length scope then you are of course well advised to use decent quality eyepieces that can handle a wide incoming light cone, eyepieces such as the Ethos and Delos range from TeleVue. There's no substitute for clean optics, decent eyepieces, and a quality well-figured mirror. A 12" should outperform a 6" in absolutely every way, and I've seen this proven with my own scopes.
I recently upgraded from a 200mm Newtonian with a .977 Strehl f6 mirror to a Skywatcher 12" f4.9 dob. I've since been able to resolve features on the disks of the Galilean moons, and I've been able to see the Pup (Sirius B). I've found that I still see more detail on the planets than I used to see with the 8" even when using the 12" in bad seeing. A good 12" scope will outperform *every* 6" scope, top end refractors included, on the planets when set up and built and used correctly.
As for the OP's point, you'll still be well able to see the three shadows, and Ganymede in silhouette against the cloudtops, and you'll be well able to see Io when it's in eclipse again silhouetted against the cloud tops. I've been able to see shadow transits very easily with my 70mm and 80mm ED refractors, so you should have no problem with your 110mm scope. It'll be small for sure, but still visible
I've been an observational astronomer for about 30 years at this stage, and I'm saving to get myself a nice 28" f2.7 Webster scope as my perfect scope, both for planetary and deep sky observations.