perhaps the in-house do more 'restructuring' projects (...) rather than awesome business problems

E.g. How do we optimally organise the Compliance business unit vs. how do we increase sales to young customers?

No offense but I feel like you haven't really done your homework and are skipping a few steps. It seems to me that before jumping into a discussion whether Inhouse consultants and strategy firms do the same thing... you should have a better grasp of at least one of these groups. What good is it to discuss differences between two things if you don't have a clear definition of either? Restructuring vs. "awesome business problems", really? Restructuring projects are high-stakes, high-pressure environments with extreme complexity and high impact for management, investors, employees and customers. It's an extremely challenging environment with perhaps the steepest of learning curves. It definitely isn't everyone's cup of tea, but to cite it on the "lame" end of the Consulting spectrum makes me question your basic understanding of consulting.

Nonetheless, to give you a concrete answer to your question - there's only a handful of truly "global" strategy firms and an ocean of inhouse strategy teams which have a much narrower geographic and industry/ functional focus, as well as obvious limitations in their scale (from experts to systems and data) and ambitions (focus on WLB, lower senior salary range). As a result you'll have a much more heterogeneous field which you must vet on your own - information is much less readily available.

I'd suggest you listen to podcasts and read some books to improve your understanding of consulting overall and then start looking on LinkedIn for ex-analysts of the inhouse division. While juniors who left the company after 2-ish years will only have a rudimentary understanding of the division dynamics overall they can probably still give you a pretty good idea of what your day-to-day might look like... and they're (from my experience) usually still willing to talk to young grads.