I can only give you my experience. I was in banking for over 20 years, in the Real Estate Loan field and looking for a new job having been laid off. I sent my resume out to a number of banks and savings and loans (back when there were S&Ls) and got a number of interviews. Two weeks later I got a job offer from the one and only bank that responded after an interview, so I took the job. It wasn't paying me what I wanted, but some pay is better than none.
I showed up for my first day of work, got acquainted, etc. When I got home that night I received a phone call from another bank with an offer 50% higher in pay than the job I showed up for. Didn't take me long to figure that one out.
Went to the first bank, told the President that I received a much higher offer from another bank I interviewed at and asked if they could meet the salary or I'd have to take the other offer. They didn't meet the other offer so I quit and took the other job.
This was only after 1 day, so I've never reported that as a previous job. Now, if you were there for a longer time period, I'd suggest doing some intensive research on the company that offered you the new position. If you leave your present position will that harm your work history? Give you bad references? Do you have to move to a different city? Is there some significant difference that the new offer gives you that you don't presently have? Are you more qualified for your present job than the new offer - where would you perform better? What are the opportunities for advancement with both companies?