I think concerts don't get their due because their scale makes their sound supremely adaptable, depending on the builder, the wood, etc. I have one that sounds indistinguishable from a tenor, I had one that was indistinguishable from a soprano, and I have one that has what I'd consider the classic concert sound described by Ukecaster. Even the scale, which you'd think would be its defining characteristic, can vary from builder to builder, from the classic 14.75" all the way to 16"--and I don't know why. Sometimes a person's opinion is determined by playing a very small number of, or just one, concert ukulele. So what any particular concert would give you that your current tenor doesn't depends entirely on the individual concert, and the tenor you're comparing it to. One easy answer to that question that's pretty much, though not always, true--especially given Tiny Tenors, etc.--is that you'll get a uke that's smaller than a tenor. That's a consideration that matters to a lot of people. I hope you can try a few concerts and see if any of them give you something you didn't know you were missing till you tried it.