So, the reasons for inhouse would be different than external, for sure. I can first speak to the latter and then give you my assumed thoughts about inhouse.
For strategy/boutique consulting, responses often fall along the following lines (not exhaustive list)
1) Skill development (okay to say you would want to eventually transfer these skills back to some other sector)
2) Working with smart people
3) Very rigorous and intellectually stimulating
4) Opportunity to work across wide range of sectors/geographies, broaden your experiences, etc.
5) Access to high-level thinking based on what you work on, who you work with.
All of the above are general - in your interview, if you can give specific examples, that helps. Maybe talk about a story you heard and why you want that experience/opportunity. I took the route of explaining how I had a very grassroots/operational focus in my prior work in nonprofits, and I wanted to build more analytical, strategic thinking skills. You don't want to put down your prior skills, but showing that you have thought about what you can gain from consulting in a specific way and how that will make you more effective is a nice touch. You can also cite specific really cool work the specific firm has done and show your passion for it -- that's a pretty effective strategy as interviewers love to see specific interest related to their firms.
For inhouse - I'm guessing here you need to demonstrate an interest in the sector/company, combined with a passion for solving problems, etc. The closer you get to a pure industry role, the more you need to do your homework on the company, it's sector, etc.