A musical/philosophical conundrum

As I was driving to work today, and I was listening to the EP my band had recorded late last year, I started realizing I am a bit torn philosophically on what I choose to play at a live show and how it compares to what was recorded. This started because I heard parts I played (and these are very small things, but meaningful to me as the musician who plays them) that I enjoyed what or how I played them, but fully realizing I don't play them that way live. Mostly because I forgot this or that small bit and when I recorded it, I was still making up the parts, or at least, the transition parts between sections were still being toyed with. When I started playing with this band, they had a set full of songs and were already gigging, so I had two rehearsals and started gigging with them. Because I didn't know the songs that well, I just started improvising parts as I felt them in the moment. Eventually those parts started sticking in my head when I heard the songs and that's how my parts began to solidify, but many things I may have played that I might have liked to keep have fell by the wayside. I have faith that the best parts stuck, though I have no proof. So my conundrum is this...do I practice and rehearse the parts as I recorded them and play them the same way, or do I leave each song open to interpretation at each performance. I look at it as a dichotomy of schools of thought exemplified by two of my fav bands: Rush and Grateful Dead. Their philosophies are at opposite sides of the spectrum. Rush writes and records their songs a fully realized songs and rarely do they ever change from that exact version, even after years of performing them. Grateful Dead do the exact opposite and tend to view recording and performance as a "this is where we are at this very moment" and it won't be played the same way again. I enjoy and appreciate both philosophies and both certainly have their pros and cons. Having the benefit of being a trained musician in larger symphonic and classical ensembles in school, I understand the "play the music as it is on the page (or recording)" aesthetic, where you have/put faith in the composer or composition...and also having the experience of playing in jazz-based ensembles since high school as well, and learning the "live/perform in the moment" school of thought. I understand the excitement and creative possibilities of never closing yourself off to inspiration, which often seems the more "spiritual" of the two. So, maybe in the end, and probably how I incorporate and straddle both ideas, is I choose the parts of the recording/song that I feel are undeniably part of the composition, and I leave the rest to interpretation and the moment. (...sometimes I know the answer to these types of questions, but I need to work through putting them into words to make myself believe or feel confident in my decisions. This is what this post is all about, I suppose.)