One big difference is that Arc is very minimal, while Common Lisp has lots of libraries and a large standard library. In Arc, you'll end up writing a lot of stuff yourself. But because Arc tends to be more concise than Common Lisp, this can be fun rather than frustrating.
In large part because Arc is so minimal, it only really has two compound data structures: cons cells and mutable key/value dictionaries.
With a bit of effort, it's possible to use Racket libraries and Racket data structures. It's easier to do this in Arc/Nu and Anarki, compared to Arc 3.1.
Arc also does not have a module system, so name collisions are a very real possibility. If your code base is small this isn't a problem, but it does make it a bit trickier to use libraries written by other people.
Another difference is that Arc takes after Scheme, so it has tail-call optimization and full first-class continuations. Recursion is quite common.
Like Scheme, Arc has a single namespace for both functions and variables, unlike Common Lisp which has separate namespaces.
Arc intentionally makes no promises of backwards-compatibility: new versions of Arc might be radically different and completely break your code. Common Lisp, on the other hand, tends to be very stable, and cares a lot about backwards-compat.
Essentially, you can think of Arc as being very similar to Scheme, but much more minimal and concise, and with Common Lisp style unhygienic macros.
