The costumes look pretty similar, for the most part. They have little tweaks that make them look newish. In the video, you can see the "Serious" dress, which looks a little different, but not by much, in my opinion, as well as the Legally Blonde (Remix) dress.
What do you think of their sound?
Here's the "First Day At Harvard" still. As you can see, her "Harvard" beater now has a pink button-up collared shirt underneath, which takes it from "ludicrously out of place" (like in the Broadway musical) to "the right pieces, the wrong colour scheme" (more like the movie). Additionally, the pink/red jeans are gone, replaced with a dark wash denim. Her boots are matte leather or vinyl, rather than snakeskin.
See all of my Legally Blonde on West End pictures here.