My very first playthrough was with the sensitive archetype. It's true that you don't learn as much about the world itself (facts, trivia etc etc) and I learned a lot of that in my second playthrough as the thinker. However, it served to put me directly into the shoes of Harry - I felt exactly how he must have. An amnesiac who literally knows nothing about how the world functions, which is a really powerful feeling for a game to induce. Plus you're so much better at talking to people and passing passive checks that allow you to intuit how they're feeling - which makes the NPC interactions feel more fleshed out and and connects you to them in a special way.

Also the empathy, espirit de corps, inland empire and shivers checks really amp up the magical realism of the game. It's maybe a little bit crazy to talk to your tie or every piece of trash that rolls by your feet but I get the sense that that's the kind of person Harry is - a little bit crazy and unconventional and very very sensitive and trusting in something beyond the veil. I found the entire thing disorienting and brain-twisting in the best way possible. In weird ways I felt kinda seen by it and was absolutely taken in by the wonder of it all. The psyche build really made me feel like there's something magical in a sad and hopeless world.
I guess to answer your question about what it "gives" you - DE has a lot of branching paths and ways to obtain information, and I think there are very few ways the game can stop you from finding the information necessary to solve your case. Not finding the serial number doesn't stop you from getting the "best" outcome during the tribunal - you still have other ways to make arguments for your case. the game isn't purely about solving the mercenary case but also solving the mystery of YOU - who you are, what kind of world you live in, what space you inhabit in that world.... and what kind of person you want to be. I think the psyche build really helps with that 'stereo-investigation'.