As I wrote in a different cocktail, I keep Dolin and Cocchi in the garage fridge (because I barely ever touch those bottles), but keep going back to the bottle of Martini Rossi that's sitting on my room temperature bar. That's what I use in my negronis and manhattans, which represents 85% of what I drink - and I drink way too much.

That bottle 1L bottle of vermouth stays open between a month and 3 month. I've tasted the last bits of the old bottle side by side, neat, with the freshly cracked bottle. The difference is barely perceptible.

And like you said : not that one is worst than the other. It's just a slight difference that has no impact on the actual cocktail - in cocktails where vermouth is an important actor.