LLB to American Lawyer

I’ve been given offers for Law at KCL and Law and Social Policy at Edinburgh. I’m waiting to hear still from UCL and LSE. Does anyone have experience with LLBs or know what path most Americans who study law abroad and want to eventually practice in the US take? Would I go to law school to get my JD after or just need to earn an LLM to be employable? Any advice/perspective is greatly appreciated