To stay put or to bug out is a great question. Its probably better to be prepared to do either one as your situation dictates. The old saying is never put all your eggs in one basket so lets say for a moment you did. You spent all your time and money to prepare to stay at your home no matter what. You have done everything to make your home virtually impenetrable, you have stockpiled food, ammo and arms, and have all the things you need. SHTF and you are doing well to defend your home out of the smoky abyss here comes a grenade you have a huge hole blown in the side of your house and begin to be over run by the people who were just as prepared as you were, what now. Well your best bet is to bug out ASAP but you have no bug out bag prepared so basically you are just taking a few things you can carry on your person. What happens once you escape? You are SOL unless your Bear Grylls.
The other end of the spectrum is you put all your money and time into a bug out bag but nothing into the idea of staying at your home. There is no economy left and nothing left in the stores just empty isles. You can bug out but where will you go you only have 2-7 days worth of food and made no attempt to build up weapons and ammunition or food, you have made no attempt to better outfit your home for protection, you are essentially stuck in your home.
This is the problem all to many people will be confronted with because they made no plan B or plan C. The best thing you can do is be prepared that's what they taught us in boy scouts and that motto has saved me countless times including being stuck in my car for 8 hours in a snow drift during a blizzard. When SHTF you will want to have a cache of food, ammo, weapons, fuel for keeping warm to stay put, a bug out bag with plans for evasion, and a vehicle that is prepared for whatever you will face. Right now is the time to plan and practice your plans and survival skills.