I've watched about 1/3 of Strang's lecture videos and several of Klein's (as well as bought both books).

Klein emphasizes practical computer science applications of LA (like principal components and hands-on coding tasks), whereas Strang emphasizes LA in terms of calculus and vector calculus.

I think both courses are outstanding. I suspect CS students will appreciate Klein's content and examples more, though Strang lectures are so good you won't find much to complain about. I have heard that some math purists object to Strang's emphasis as being as lacking fundamental rigor and overemphasizing intuition. But this criticism probably applies to both courses. I think both approach LA in terms of its utility toward CS (Klein) or engineering (Strang) problems.