I too have both. Many trim class routers. A couble dremls with a plugne and fixed router based.
*** Ask what would be better for inlays... That was the question ask by OP.
A Dremel makes a good rotary tool for quick detail work... but I've never thought of my Dremels as a tool that removes much material at a time, nor something I would use for extended periods of time. The bearings get hot when trying to route for very long. It doesn't take a load very well, so you have to make very shallow depth of cuts. The adjustments for depth of cuts are rudimentary and not made for precison (more for abut this much kinds of adjustments). The router type bits for a Dremel ar every limited.
A Trim router has more power and is steadier. Being steadier, I find it more consistent and easier to get an accurate cut.
I use both, but each has it's pro's and con's.
"Don't worry, I saw this work in a cartoon once."
"Usually learning skills and tooling involves a progression of logical steps."