Not really, not necessarily. Many corporate strategy teams are loaded with MBB talent, so you will get to learn a lot of things. Much will depend on your hierarchy also, but there is definitely the potential of interesting and influential work
Also - the Big 4 consulting cabinets aren't all equal. Strategy& or Deloitte Strategy are better for example.
At the end of the day, you are really asking about consulting (across industries, locations...) and industry (one industry, typically less travel). More than whenever one is a step up over the other therefore, you really want to ask yourself about your long term and lifestyle goals. You are right, very few big-company jobs will ever be as exciting / high energy as Strat consulting.