LAPD: One of the best police departments in the entire country. A lot of people (myself included) greatly respect the LAPD for the work they are doing in protecting this city. Being an LAPD officer means being out on the streets, dealing directly with the citizens of LA. LAPD officers are sharp, well-trained and well-prepared (as a general rule).
LASD: I don't know much about the LASD. They do work similar to that of the LAPD, but in my limited experience they have more restrictions. In my personal opinion, I would rather work for the LAPD, and in fact hope to one day. It seems more exciting, fast-paced, and I want to protect the city that I was born and raised in. You could go on their respective websites and do some more research. Law enforcement careers entail much of the same training and whatnot, from what I understand. Good luck!
teenager who has lived in LA her entire life :)