The LG 5k and Studio Display use nearly identical panels and in reviews (both users and reviewers) they are nearly indistinguishable. The Studio Display essentially is the same monitor with a new case, better speakers, different webcam, and far higher price tag when adding height adjustment (which came on the LG).
The ASD is brighter than the LG 5K. Not only is it listed as a 100 nits brighter but it's also been tested at 686 nits peak brightness by the Tech Chap on YouTube. It also offers a nano-texture option (if desired) which the LG does not.
Personally I would recommend the ASD over the LG as you will receive superior support from Apple (and easier if you have an Apple store local), the casing of the display is much nicer both physically and visually, and of course the display itself is brighter. The LG has a free height adjuster versus the $400 premium on the ASD. One could also use a Vesa mount or get a stand to place the display on top if desired.
I feel the speakers are a moot point honestly. Despite Apple's claims and what some reviewers have written, they are far inferior than a cheap pair of 2.1 speakers. The webcam is a letdown but I do believe Apple will improve this in a software update.
Whether these differences are worth the higher price tag is an individual question.