What is the right way to convey the meaning that I want to say?
Your job is worse than mine, so I am not going to quit my job.
Is there a better choice to say this? Should I use less better than instead?
Your alternatives might probably be worse than and not as good as. I know what you mean by less better than, but sadly, that's not a proper phrase.
Worse than puts your job a rank below my job, while it puts my job itself into the bad class.
Not as good as also places your job a rank below my job. However, in this case it places my job in the good class.
In my opinion, the only possible meaning of "less better" would be "better by a smaller margin." In other words, if X is a lot better than Z, and Y is just a little bit better than Z, then Y would be "less better" than X.
This is a construction for which I find little use.
Furthermore, note that "less better" does not mean "not as good." In my example, both X and Y are better than Z, albeit to different degrees. Neither one is worse. Therefore "less better" cannot be a synonym of "worse."
Simple answer: Do not use "less better" at all.
The phrase "less better" would never be appropriate in this context. "Better" is a comparative. At least in my opinion, anything which is "less better" needs to be "less better" than something. For example, if you were comparing Person A's job and Person B's job, to Person C's job, then you could write "A's job is less better than B's job [compared to C's job]."
In this case, you could use "less good," but that's an unusual formation. "Worse" however, is a much more common formation, and I would recommend it.