Public or Private CNA?

Hi everyone. I have some questions about whether to work for a private or public nursing home as a CNA. I am nearly finished with a CNA program, and I have applied for a job at the facility where the training takes place. It's run by the state, but it is taking a long time to get my application "approved." There are many private nursing homes nearby that take less time to approve someone for a job, but I've heard that it's better for CNAs to work for the state (because of better benefits), so that's why I haven't sought out other jobs yet. Is that really the case? Also, do most private and public nursing homes pay CNAs more when they work on weekends, midnight shifts, and holidays? The state-run place pays the same rate for weekends, but pays time and a half for holidays. Are there really any differences between how private and public nursing homes are run? Thanks! :)