Both signal an improvement. While "better off" could imply a financial improvement like "well off" it does not necessarily mean wealthier from the sentence itself. "Better off" could simply mean happier or that the work is easier. In short, it was a good decision and the person has improved certain aspects of their life-the specific aspects depend on the context/speaker.
"I am much better now I have this job" to me has two implications. The first: an improved health or they are better now/more competent (at something) which isn't stated in the sentence. Saying "i am much better now" does not imply better finances.