Composition by writing out rhythms and chords, and writing out multiple parts for multiple instruments, is just a different experience than playing it out on a keyboard. It lets you put more thought into how things line up and are organized, versus how they sound. That sounds downright unmusical but it's a big difference, I think.
This is just from my limited experience as a hobby composer sitting in front of a keyboard with pencil and staff paper, but I've heard it from other composers I know as well.
I did it with synthesizer and computer. What you say is still true, though, since that probably qualifies as yet a third way of composing.
For that matter I instantly noticed a difference going from ScreamTracker to a MIDI synth, too. Didn't even have an acclimation period, it was immediately of a different nature.
This is just from my limited experience as a hobby composer sitting in front of a keyboard with pencil and staff paper, but I've heard it from other composers I know as well.