as others said, despite what a lot of people believe in, a ligature is a simple device designed to securely hold in place the reed on your mouthpiece .
You can have ligatures fitting a mouthpiece/reed combination better than others and more importantly the ligature has to be comfortable to the person using it.
I personally prefer, if possible, one screw ligatures. I never understood or heard any real difference when a ligature offers different pressure plates but I do have the slight impression that a soft material leather like ligature like a rovner (without pressure plate) allows for a slight difference in sound (which I find positive on my soprano Ponzol mouthpiece), the rest...... they all sound the same to me and I only care whether the reed doesn’t move too much left-right-left-up-down and if I can tune it without destroying my hands or dislodging the reed when tuning.
My current favourite is a Brancher wire ligature although on my Ponzol M2 alto mouthpiece I have to use a Berg-Larsen because the Brancher that I have bought for it is a bit too loose.
So, in answer to the question posed by saxofon, it is fair to say that approximately 41% of sax players in a recent poll did not think that any ligatures are particularly better than any others, as long as they hold the reed firmly. 59% in a recent poll thought that there was a different sound produced by different ligatures, but that this may be quite subjective for many of the players who could hear a difference.
It is perhaps an idea to buy a few ligatures and see what you think, personally. My preference is for metal ligatures which seem to result in a brighter, livelier sound from my point of view, and I like Marc Jean ligatures best.
It is a controversial area for sax players and good for you to come to your own conclusions.
In the interest of full disclosure it was 41% of 186 who couldn't hear a difference through computer speakers of a recorded saxophone using unknown equipment.
62% of 260 voters thought it was important to find the right ligature.
For me it's about security, continuity, range and flexibility of tone combined with ease of use.
Different perceptions from behind the mouthpiece may be not be detectable by the ear of the listener but the confidence generated by the feel of the setup will improve the performance by not distracting the player with technicalities and practicalities.
I had to adapt a bought ligature to fit the vintage tenor mp I'm playing at the moment. That's currently the best one for me.