The question we want to explore is, "Are they all the same?" and "Is there any reason to buy one of these expensive upgraded ligatures, or should I just use the one I have until it gets old?"
The most basic ligature design task is to simply hold the reed, securely to the mouthpiece. Most basic metal or fabric ligatures will hold the reed just fine when sized properly. Fitting metal ligatures can be complicated due to shape differences. Leather or fabric ligatures will fit a much larger number of mouthpieces because fabric will fit the shape of any mouthpiece with a similar size. The reason fabric ligatures have become so popular in recent years is that they fit so many mouthpieces, they don't have shape issues when fitting, and are less expensive than metal ligatures. This makes ordering them online really easy too.
Rovner was the first company to create these fabric type ligatures and there are many different designs now available that affect the tone on the saxophone. They say a picture is worth a thousand words and 'they' are right. You can find ligatures with metal plates at the reed's point of contact, cut outs in the band of fabric where the reed is held, and simple designs with full contact all the way around the mouthpiece and reed.
The darkest sounding is a solid band due to constant points of contact on the reed from the fabric. This will also affect the volume, making the sound darker and softer. The metal plates create a better conduit for vibration and tend to open the sound up a little more, and the cut away reed design maintains a solid connection to the mouthpiece while freeing the vibration of the reed with less material tying it down, and these sound a little brighter.
I like the single screw design on the Rovner style because it is a reliable, quick adjustment when adjusting your reeds. There are single screw designed ligatures made of metal also, like the Vandoren Optimum ligature, another personal favorite, and my main ligature for clarinet.
With all this said about Rovner style ligatures, I have to say that I don't play them very often on any of my single reed instruments with the exception of my jazz alto set up. I use the metal plate design; a Rovner style ligature made by my mouthpiece manufacturer.
Metal ligatures have the same options: one screw or two, different design points of contact, and basic trade-offs over contact points and security of the reed staying in place.
The Ultimate Ligature is designed to optimize all possible vibrations and allow the reed to sound the best it can. We first notice a very limited amount of contact with the mouthpiece, and then a floating plate holding the reed for maximum vibration. Problem is, if the sax player needs to adjust the mouthpiece at all, a simple adjustment will likely shift the reed out of place, and getting it straight again is not very easy. I retired my Ultimate Ligatures after a few months.
The best ligatures will do the job and not detract from the tone. My favorites today are the Vandoren Optimum – metal, one screw, secure, floating plate on reed, and point of contact points can be changed with included, extra plates. I also love the BG metal ligature for sound and design reasons.
I don't think a ligature can make a weak mouthpiece play great, but do believe a great one will take a great mouthpiece even further.