I imagine there would be a significant difference in mental engagement when playing different kinds of instruments. Drums vs monophonic instruments vs polyphonics engage an ever increasing range of musical fundamentals and skill: from only rhythm and volume to a single line of melody to multi-line and harmony.
A similar range of engagement (and control) may be needed to play instruments with fewer vs more degrees of freedom (three valves on one hand for a trumpet vs all fingers of both hands for a clarinet (yet monophonic) vs both hands for guitar or violin (asymmetric) or piano (symmetric) (all polyphonic). Instruments that make melody without frets also seem like they'd be more demanding (and more engaging) to play than those with. Instruments that allow more subtlety of expression should be more demanding cognitively too, like the human voice.
I would imagine learning to play more complex instruments is more difficult later in life too (than learning to play those less complex), since the older brain is less plastic or absorbent.