Uhm. I'm divided. Common Lisp it's the weird cousin, bloated at first but in the end you get SBCL, ECL or CCL and almost everything will work the same. With Scheme, you need to instal SRFI's to complete SICP exercises and then there's R5RS and R7RS.
You have no way to run Hypergiant under Guile. In Common Lisp, tons of packages for QuickLisp/UltraLisp will run on SBCL, CCL and ECL with ease.
In the end Scheme+Dependencies can be more convoluted than a subset of Common Lisp (you can avoid CLOS if you don't need it for instance).
I've never really heard of installing SRFIs (could be my ignorance); do you mean importing them? Or is installing SRFI implementations as their own packages really common? (Haven't really tried R7.)
The anti-R6/R7 folks (or what I've heard) won't see a problem so long as you can use CL to build fancy serious software, which lets Scheme stay small and simple for education. (Of course ideally you'd be able to do any SICP exercise on a Scheme implementation out of the box, though.)