Having grown up in Los Angeles and moving away in 1995, I'm surprised you haven't asked this question much sooner! I had the opportunity to move to Omaha as an Insurance agent for Mutual of Omaha in 1986 and at that time, the prospect of Omaha NE was enough to send me over to Prudential Insurance Company instead.
Everything is relative. In comparison to L.A. (depending on where in L.A. County you are) the same buying power will yield a much better home. The southwest has been growing tremendously. The quality of school systems also is subjective to your children's needs and your desires. Regardless, of Omaha Public Schools, Elkhorn, Millard, La Vista/Papillion or Gretna districts. Your best option would be to research the free school reports. For ease of suggestion, those can be found on my site www.Talk2Teri.com . If crime is a concern (I can relate to the L.A. frustrations) then your best source of information would be the Omaha Police statistics and/or the Douglas or Sarpy County Sheriff's Department statistics.
I would love to personally address any or all of these issues with you one-on-one. Just visit my website or email Teri@Talk2Teri.com or call my cell directly 402-689-4041. I would love to help another Los Angeles bailer!