When would you hire an Independent Technology Consultant over a consulting agency?

Good question Bobby. Being that we're an independent business intelligence consulting company (www.decisionpath.com, if you're curious), we've got pretty good visibility into both realms.

Broad generalizations (and again, this is specifically in the business intelligence and analytics arena):

Big consulting firms often look to fit a client into their pre-defined solution (often able to "prescribe" before really diagnosing) -- they've got really sharp people who are great up front at defining a problem and scoping a solution (so long at it fits into their model). This enables them to turn over actual technical implementation to relatively junior analysts who can follow the model well, but can't deviate in order to deliver greater value (i.e. value in evolving and adapting a project based on deep domain knowledge).

"Lone wolves" like yourselves are probably really great at either thought leadership or technical implementations, but are fairly limited in scope of work (just because the resources aren't there to be good at both... generally speaking). Also, because of lower overhead ITCs have the ability to drill down into a niche and develop deep domain expertise for that specific area (risky as it is to have such a specialized area of knowledge).