I'm seriously considering relocating my family from D.C. to LA. What can I expect?

I'm a single Mom of two and I'm thinking of moving this summer to accept a position in my field of work. D.C. has it's share of crime but is LA worse? In terms of crime what areas of LA should I stay out of, what are nice areas to live in under $2500/mth? Overall what can I expect coming from a city like D.C.?