I'm sorry to hear of the situation.
I'm not sure what your new employer is thinking, but under CA law, non-compete agreements are almost all illegal and unenforceable.
CA Business and Professions Code states in pertinent part: §16600. Except as provided in this chapter, every contract by which anyone is restrained from engaging in a lawful profession, trade, or business of any kind is to that extent void.
Here is a link to the few exceptions---which do not reach to individual employees like yourself:
As non-competes are not legal in CA, if you are terminated from your job because you refuse to sign such an agreement, you may well have a valid claim for Wrongful Termination, as well as being eligible for unemployment benefits.
As for whether the increase in wages will compensate for the lost benefits and reimbursements---only you can decide whether that is worthwhile to you.
If you consider a lawsuit, you will want to consult with a local Employment Law attorney to assist you.
I hope you found my answer informative.
I wish you the best in 2012.