A bigger truck is never a bad idea, especially if you have a larger payload (family counts as payload).
5th wheels do have built in towing stability with their hitch being right over the rear truck axle. But they have hitch related issues that can pop up too. And they cannot be taken off road as far as a trailer. They have more storage and more livable space per foot than a travel trailer. 5th wheels are typically much taller than trailers, thus restricting where you can take them. They don't track very closely behind the truck, requiring that you swing wider on tight turns. None of that is probably important if you stay in commercial camp grounds or RV resorts. Quite often you can back a 5er into a spot you would never get a trailer.
Travel trailers have some specific requirements, like 10% - 15% of total weight must be on the tongue to avoid sway, which can be very dangerous. That tongue weight counts against truck payload too. An anti-sway hitch should be used in most circumstances. A weight distributing hitch helps spread the tongue weight back to the trailer axles and to the tow vehicle front axle. There are many hitches that incorporate both features. They come in many brands, performance levels and prices. Travel trailer height is usually a foot or two lower and will fit under various obstacles that a 5er can't. Travel trailers have much less outside storage and usually less inside storage. They track pretty true behind the tow vehicle, which will allow you to go on narrower, twisty roads. They often don't have very good ground clearance and can be damaged if you're not careful, all of which is easily correctable in most cases.
A travel trailer allows you to use an SUV as a tow vehicle. It also allows you full use of your truck bed, for those larger toys.
I'm still on the fence about which platform is best. When we were younger, a travel trailer was less expensive and was definitely the better choice for dragging out into the woods and crossing creek beds, etc. As we have become empty nesters and are feeling our age, we're starting to lean more toward longer journeys and nicer, established campgrounds and resorts. A fifth wheel might be much more appreciated.
