Let us cut the "fps is noticeable or not", as above 60, it tends to be a case by case thing.
The only thing that really benefit from a crazy high fps is the controls, as they are way more tight when checking each 50ms instead of each 200ms, and will be noticed by anyone trying to do fast input.
That said, minecraft is not designed to be a fast-paced game, and it tends not to take well the fast inputs sometimes, resulting into stuck keys and other double click problems.
It is, however, very impacting in games like first person shooters, platform (meat boys?) or action games, and basically any game where precision and fast reaction is rewarded.
the problem we have here is a low and/or fluctuating fps, that makes the game a little hard to play, because the timing and delays are no longer constant. (skeleton shooting arrows, furnaces operations, vegetable growth etc)
For low-end computers, the fact minecraft also runs a server now will impact the performances, as it needs to do more computations, and for that, even the mighty optifine won't do a thing.
The only thing you can do is to remain with the default texture pack and put optifine, it will considerably boost your fps, usually at least.