I had a job offer before being let go from a previous company. My question would be in future job interviews, should I tell them that a better opportunity came up or I was let go? It's a tricky question because I want to be truthful the same day I was let go I was going to resign. Just to give you more context, HR said company has a policy where employees are not allowed to give references. I was terminated without cause, it's more of mutual agreement since it was not what I wanted to do as a career and they figured that out.
If I were hiring, and you told me the story that you were let go the same day you got a job offer, and it was not for cause, I'd want you on my team. It demonstrates that you were able to read the situation and take action accordingly.
That has a real value in business. Be honest and tell them why you went searching for another opportunity to begin with. If you can articulate how you saw trouble coming for the company, even better.
It all depends on the reason for your being let go. Keep in mind this will most likely come out when they contact your references.
Either way you should work the event into your explanation.
If the company was down-sizing and, knowing that you might be let go, you went and got a different job then that's fine. Simply say so.
If you were dismissed for cause, and were looking for a new job before the final decision to fire you was made then that's a little trickier. It's very likely that the new place will find out what happened, so you should preempt their queries to your former employer's office with an explanation that takes the edge off of the event.
If you were let go, because company was not performing as expected and was in financial trouble, it is not a big deal and happens to the best of us. Companies fold and employees were let go, sometime all of a sudden, sometimes slowly. All employers understand this. On the other hand if you were let go due to something that you did wrong or not do, causing the company some harm, that is a different story. Because, when your old employer gets contacted for past position reference, they might say (in US this is highly unlikely as they are afraid of being sued) you were terminated with cause. If termination with cause is your case, you might want to state that at a future interview, instead of putting it on your resume like the Scarlet Letter, and provide an explanation why it happened, how you addressed the situation etc. It might be taken as a learning experience and some employers may even like your honesty and a lesson learned.