Materials, craftsmanship, performance, options in lofts and grind (although the other companies are starting to offer more now), and multiple finishes. There is a reason they are by far the most used wedges by professionals and amateurs. They are in the bags of many professionals who have other company's club contracts.

With all the lifts and grind options, better players can fine tune their clubs to match their short game. Those that just want a 52-56-60 set to use with 2 piece ionomer balls won’t see much advantage.

Im not a big cally wedge guy so, aside from the new style of angle cut micro grooves, beyond that I cannot tell you ( from my own testing through, I find they disrupt the spin characteristics from the actual grooves on the club face).

I like that Vokey wedges offer soooo many different combinations of loft, bounce and grind options. cally certainly is a close second when it comes to grind and bounce choices, but I personally feel like Vokey Wedges are a bit more precise with the combinations. I do however wish they offered the pre-worn leading edge as a standard option and not an upcharge through WW. I do like that feature on the Jaws Wedges and, the TM MG4 wedges as well as the TW grinds on the MG3's. That being said, it's not enough to get the SM9's out of my bag.

I can't tell you how they are different than another brand because i have not hit them. However I can vouch for the consistency and quality in the product of a Vokey. First off there are so many options in lofts, bounce, finishes and grinds, Theres definitely going to be plenty of choices. Then you can factor in the years of design and research that titleist and Vokey have put into these wedges using tour pros input. When you set it down to hit a shot its a beautiful club that has all the research and technology you need to believe you will hit a good, consistent shot.

Same reason we play Scotty putters over all the others. Craftsmanship and name are enough to keep me swinging

Originally played with Ram Cobalt wedges, changed to Vokey wedges when the time came to replace them, never tried any other wedges since then, probably gone through around five or six generations of Vokey since then.
Always gone for a 52F & 58M combination, I tend change the 58 every year or so as I use it out of bunkers etc. and it tends to wear more, the 52 not so much.
Since the SM6s I've had the custom fit options and have the same shafts as fitted in my iron set rather then the standard wedge shaft.
What I like about Vokeys is their feel, quality, numerous options in the range although I tend to stick to the same grinds and finish as they work for me.
I only wish they would sell a 54 wedge with a M grind in the UK, I've enquired but apparently they are only available in the US!