I've been both an internal consultant and an external consultant at various times in my career. My preference is for internal consulting and I'm often asked why: people seem to find it curious as 'internal management consultancy has traditionally been seen as the poor cousin of its external counterpart', (and still is in many quarters).
I like it because I get to know the organisation as an employee: I experience it in a way that an external consultant can only approximate – its style, culture, leadership - and yet I also have to keep a certain distance from it. It's a tension that means I both consult and have to live with the consequences of the work that I do and learn from it in a way that external consultants don't. I like that insider/outsider role challenging though it is.
Reading lists of pros and cons of internal v external consulting you get a feel for the differences. They're well explained, for example, by Consultancy UK and 9 lenses. What's interesting is that in this kind of comparison they are presented as a kind of either/or. There seems to be a tacit implication that you use internal consultants for different types of assignments than the ones you use external consultants for.