There is not a simple answer to the question. Much depends on your situation, your familiarity with campers, geography and type of crisis you would be dealing with. Type of campers would include motor homes, travel trailers and truck campers.
When people think of bug-out-vehicles (BOV) they think of a vehicle that can get them out of a dangerous area quickly. The vehicle is packed with emergency essentials and is ready to go at a moment’s notice. Bugging-out signifies haste, leaving an area that has become hostile, and that means leaving by the fastest and safest means possible, does a travel trailer or motor home fit that description. You can decide that based on a multitude of factors.
If your home was destroyed by some type of a disaster and you had a camper/motor home then you have shelter. However, if the disaster has not struck yet, but if one forecasted or predicted and you feel you would have to bug-out, would you jump in your camper. If you did, would you be able to get clear of the area driving a motor home or pulling a trailer, versus simply getting in your vehicle or setting out on foot, this is the question you need to answer, and can you answer it before a disaster strikes.
If you have a travel trailer, this means you need a vehicle capable of pulling the trailer, and keep in mind during a crisis you would probably overload the trailer, which in turn would put more stress on the vehicle pulling it. Tires, engine and transmission all would be under more stress.
Water and fuel alone would take up considerable weight and then there is food, generators, clothing and other essentials, and because of the space, available people would tend to pack more. If you could not leave well ahead of others that are fleeing, you may find the highways are gridlocked, and you would essentially be trapped with all of your supplies in one place.
On the other hand, if you managed to get out of the urban area, you now have a shelter for when you arrive at your bug-location. You do have one of course, or do you plan to pull into a rest stop or camping area, during a crisis.
Rest areas and campsites would be overwhelmed in most cases by others doing just what you are doing and of course looters, and other criminals will go where the valuables are. If the crisis were, a natural disaster, campsites and rest areas may not be ideal places for sheltering.
How would you refuel, if you did manage to get to a bug-out location or any safe haven? You can carry fuel with you but the amounts would be limited. You simply cannot end up somewhere without the ability to leave that area at some point, and have to leave your home essentially and all of your supplies behind.
Truck campers would be better suited as a bug-out vehicle, because they are self-contained but you are limited on space. However, you would have more storage space than a typical vehicle. The truck camper would provide you with shelter, and they can be maneuvered around obstacles much easier than a motor home or travel trailer being towed. Of course, as with a motor home or travel trailer, they would be obvious targets for looters and others.
Campers or motor homes would be ideal for off grid living and in some situations could be used during a crisis if they were set up before the disaster struck. A camper would be the same as having a shelter built at your bug-out-location. Of course, you need a location that is remote and one you had access to at all times, in other words, you would have to own it to ensure you would not be uprooted in the middle of a crisis. Even if you did own a piece of property there are no guarantees you would be able to hang on to it during certain situations.
One of the advantages of having a camper is storage, in particular storage of safe drinking water. This is provided you filled the tank(s) from a clean source. You would need water hoses rated for drinking water and you would have to know the source is safe. Filling the tanks with contaminated water means the water would have to be drained and then the tank(s) sanitized properly and this would take large amounts of clean water.
Mobility would be a problem with any type of camper, so taking to the open roads for any substantial distance would be problematic. You would need more fuel for the towing vehicle, than you would otherwise need when it was not towing a trailer and fuel for the motor home. This could become a problem one that could not be solved easily if at all during some situations.
You may be forced to abandon your camper at some point and if so you would need a vehicle so having a travel trailer would have its advantages over a motor home, because you can unhook the towing vehicle. A pickup camper would make the most sense but you would have to consider its downfalls as well.