This is too general a question to give a comparative answer. I can think of 7 or 8 quite different designs off the top of my head, and I'd guess there are quite a few more, each with a number of variations.
As a general answer, a bridge must achieve a number of things:
1. It must stay attached. If it's glued to the top this means a minimum glueing area. But a floating bridge can be tiny if the tailpiece is fixed.
2. It musn't be too heavy, or too light, or taake up too much of the top. Too heavy can damp the top, making it quiet and dull. Too light might not transfer energey efficiently (I think, but others will know better - certainly it can affect tone adversely). The more top it occupies, the less there is to vibrate and make music.
3. It must be strong enough not to fall apart under string tension.
4. It must put the terminations of the strings in (approximately) the right places.
5. It must transmit the energy of the strings to the top as efficiently as possible.
All bridges make compromises between these. As an example, a floating bridge is light and occupies very little of the top surface area. But it's less effeicient than a fixed bridge in transferring string energy. I'm just finishing a sopranino with a floating bridge, and to compensate the top is very lightly braced with no bridge plate. As a different example, if you use a pinned bridge you need a robust bridge plate to stop the strings pulling through, but the plate takes a lot of the load so the bridge footprint could be smaller (except you need the space to fit the pins). And so it goes.
Then you start making aesthetic choices, which give you different shapes, and choosing your wood for a combination of its appearance and mechanical properties, and on it goes again.
Really, it's remarkable that any builder ever decides what kind of bridge to use.