Different strokes for different folks - and a mix of different types is often necessary.
I remember the very first time I ever completed (through by work at the time) a psychological profile. (I know such things are mostly discredited, but bear with me). I think it was based around Belbin's team profiles.
I came out as a creative, innovative, 'starter' of things - which actually matches me pretty well: I'm excited by solutions and new ideas, but I often don't complete personal (and sometimes professional!) projects 100% - I've lost interest and moved onto the next shiny thing by then. (Professionally, I'm best with a complimentary team around me.)
A colleague who I got on well with but also often found frustrating, came out as a 'completer finisher'. Which again aligned well with my observation of her and her own testimony of where she drew her gratification from, and also explained why I sometimes found her frustrating: because we were total opposites in this regard.
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Anyway... maybe the situation you describe on your team is explained somewhat by this? You both want to work on aspects of a project that you find gratifying - but you derive gratification from different aspects?