While Clojure is definitely more a in-thing right now, it's nice to see "the originals", where it all came from. There are several things Clojure does really well, at the cost of other aspects. It's a very opinionated language, and for some, it may be too opinionated. I find idiomatic Clojure-code to be a bit on the too terse side, affecting the clarity of the code.
Let's also mention the JVM. While this is often used as argument for Clojure, it can also be an argument against it. Now your application needs a JVM to run. That excludes my Raspberry from ever running it, unless you find 30 seconds+ startup time to be acceptable. I don't.
Looking into Scheme, you will definitely appreciate the simplicity of the language. Unlike Clojure, there's no magic behind the curtains. What you see is what you get, and yet it's still so capable. That's quite eye-opening and magic in its own right.
Scheme however isn't a standardized language, like Common Lisp. In that regard you cannot guarantee that what works in one Scheme-implementation works in another. With Common Lisp you can do that. And from that point of view, it makes sense to have a good story on modules/packages. And Common Lisp has that. In plenty.
In Clojure, with Leiningen, you can easily declare what dependencies you have and have those fetched build-time without any extra work what so ever. Sounds good, eh? In Common Lisp you can do that in ordinary code, runtime, even in the REPL. Your code just declares what it needs, and it's there. Just stop a second and think what that does to extensibility, when software written in CL lets you plug your own code in.
All in all, once you know a LISP looking into others is much less work. And as such, you should definitely check out others. Maybe there are other LISPs which suites your needs even better? Unless you look around, you will never know.
Scheme is a standardized language. The first standards defined a relatively small language, also useful for teaching purposes. Then it was tried to define a more modern Scheme with a core language and a library. The R6RS standard was kind of controversial and now there is work for quite some time on R7RS. Additionally the Scheme community has a process to define extensions. Generally the landscape of Scheme is quite a bit more fragmented than the CL landscape. The implementations can differ widely in their implemented language. But if you look at individual systems, Scheme systems have to offer quite a lot. Also, historically there are a several really excellent Scheme books for learning programming and/or computer science.
This site, news.ycombinator.com , actually is written in a Lisp dialect (Arc) running on top of a 'Scheme'.
Armed Bear Common Lisp http://abcl.org/ is a JVM Common Lisp with this feature.