I would contradict the primary premise of the first answer. There is no such thing as "better". You need to be able to execute both techniques, i.e. muting the other strings and letting them be open. So in reality I'd say you must practice both ways. The true answer to your question will depend on whether your are playing electric or classical acoustic guitar.
In the world of an electric shredder, with oodles of reverb, delay, and distortion/overdrive letting an open string be un-muted can lead to an aural catastrophe as they will not only ring with the fretted notes but that "ringing" can be amplified by the coupling between the strings and the pickup, made hotter by the effects set up. If you are shredding with no effects, or little effects, like a Jazz guitarist with a clean set up this issue may not be as severe.
On the classical guitar most authoritative resources will tell you that you must be able to execute the movements of your left hand without touching the other strings. This is because you will eventually come to arrangements of pieces that require you to hold a drone note one one string while fingering a neighboring string. And this can happen on the string above the one you are fretting. So it will be necessary to execute scale patterns on one string while letting the neighboring string ring, or even hold another note, or tremolo the note. Getting used to letting your fingers drape over the other strings to mute them is poor form in some circles.
But, this is why I point out that both are important. Depending on what you play will need to be able to do both. So the real question is which is easier? In my experience and "opinion" it is more difficult to execute these exercises with the finger NOT touching neighboring strings and for that reason I'd err on the side of trying your best as a beginner to execute the exercise in a manner that requires the greatest precision. Relaxing the fingers later to mute neighboring strings is much easier than acquiring precision later.
