As Vlad said - strategic planning has nothing strategic about it. You will mostly track results & report on them, creating pretty slides and building pretty decks to tell execs what happened. In other words, you are an expensive paper pusher and add nothing to the company. Be prepared to work evenings and week-ends also if there's a big presentation coming. Only upside basically is you will have high level visibility, which you can parlay into fast-ish career trajectory.
Corporate Strategy on the other hand, will typically have you work on high visibility projects with a significant potential impact on the company. Work isn't nearly as interesting as MBB work (usually), but definitely beats corporate planning from a variety and learning perspective. Career is steeper, work is more interesting, you see the impact of your work... I think it should be clear which one I am leaning towards :)