In my opinion, as someone that does interviewing and hiring, it completely depends on the reason. If you are being laid off because the company is downsizing, a contract ended, or something of no fault of your own, there is nothing wrong with that. If you are being fired due to wrong doing, it would be best to resign so you can honestly say you resigned rather than explaining why you were fired. That being said, you would still need a reason to give if asked about it. You would need to know what you were going to say before your interview so that it flowed naturally. Thinking about a reason on the fly because someone asks about it could be noticed by the person doing the interview.
When I interview anyone, I go through all of their listed employment history and ask them why they left each place. There are good and bad reasons to be fired or to resign, so answer wisely.
Personally, saying you were bored out of your mind due to too much down time, would be a turn off for me. My instant reaction would be, why didn’t you find other things to do with your down time. When my employees have down time (which is rare), they are expected to find other things to do, such as helping other employees, helping cleaning up the unit, stocking supplies, and more. However, being bored of the repetition and looking for change is difference. It’s all about how you word it.
What is the reason you are being let go? Perhaps sharing that with us would help us find the best option for you and explanation to give.
In regards to unemployment, yes, resigning means you wouldn’t get unemployment. Being let go does not guarantee you will get it either though. I work for a company that fights all unemployment claims.