Heavy cargo on a bike can raise the center of gravity. With smaller cargo, whether one uses a trailer or attaches the cargo to the bike (cargo racks with straps, panniers, a backpack, et cetera) is, to a point, a personal preference. (I don't know if there are recumbent cargo bikes, so I really can't comment on that.)
However, when the cargo gets large enough, a trailer will become the best option for a couple of reasons:
- A trailer has more room than a bike's racks, baskets, or panniers. Particularly large items simply won't fit well on a bike's rack, or at least not elegantly.
- A trailer will keep the weight lower to the ground, keeping the center of gravity lower.
- Good-quality trailers can last a long time, but can be expensive.
However, panniers and racks have the following advantages:
- Flexibility. One can bring four panniers along (or six on a bike like the Big Dummy) or just one.
- Some bikes handle better with panniers on them
- They have limited space, and can wear quickly.
- Racks are difficult to attach on some bikes, particularly a bike with suspension or without rack eyelets on the frame. Solutions do exist for both of these scenarios.
Baskets are another option.
- They have the advantage of ease of use: the user can toss stuff in the basket and roll away.
- However, stuff can blow out of them, and they're heavier than panniers.
There are bikes that are built for cargo, such as the Surly Big Dummy (essentially a bike with the frame behind the saddle stretched out for better cargo placement) and box bikes. Also, there are industrial tricycles with room for large baskets in the back, designed to tote around large tool boxes and other, similar heavy stuff.
It's probably impossible to say what style of bike is best for large cargo. That's why I have several bikes, some good for hanging panniers from, some good at pulling a trailer.
Recumbent bikes can and do carry panniers or pull trailers. However, I've never seen one with any kind of basket. Perhaps someone else can weigh in on this aspect of the question?