I'm not a big fan of ponchos, but I really like tarps. It seems to me that people are attracted to ponchos because they appear (in theory) to be a multi-use item, which can serve as both raingear and shelter.

Regarding ponchos as rain gear, I find that in the terrain and conditions I often operate in they don't really work very well. In particular, they are very poor in windy weather. Also, as hikermor notes, they don't work well in brush, or any sort of rough terrain. I flat will not rely on a poncho as my primary weather protection. A proper weather resistant jacket, cut roomy enough to wear over insulation is a vastly superior choice, in my opinion. Add rain pants for very wet weather.

For shelter, as unimogbert found out, most ponchos are too small to rig very well. One could make a bigger poncho, but that would make it even more of a hassle as rain gear, at least in the wind. One could put two ponchos together as Montanaro suggests, but that requires carrying even more stuff.

A small, light weight tarp makes a much better shelter, in my opinion. Lots of option in how you rig it. If two of you are together, you can put one tarp under as a ground cloth, and rig one over you as a shelter.

EDIT: I should add that I mostly carry the tarp only for SAR missions. Besides emergency shelter, a tarp can be rigged in various ways to serve as a litter, or as a toboggan to drag an injured person on the snow.

For casual day hiking, I don't generally carry the tarp. Instead I always have a SOL Emergency Bivy stashed in the bottom of my pack. It only $17, weighs 3.8 oz (108 gram), and takes up a tiny volume in my pack. It, together with proper clothing, will get me through the night.

That's my view, for whatever it's worth. As always, others may have different opinions and find other solutions.