How do I create concrete or fiberglass outdoor seating that will last?
Concrete will definitely be strong enough if done right.

Make sure you use the right mix.  I would use sakrete 5000 plus, NOT quikcrete 5000, and add a hand full of Portland cement to better hold the mosaic.  Then add superplasticizers.  More water is bad, but you want it to flow into an odd shaped mold and around mosaic tiles, superplasticizers will solve this.  You can get this at http://www.expressions-ltd.com/default.asp You can get some integral coloring for the concrete there too.

The forms will be tricky, but i think i would build a wood box and drape some cloth in it the way you want.  Then spread some glue on it to stiffen it up.  Then use bondo and sand it down to smooth.  Then you can use some spray adhesive or silicone to put your mosaic tiles in upside down.

You are going to need to vibrate it after you pour it.  Maybe just hammer on the wood box.

I am saying this would be solid concrete, but this will be very heavy when you demold it.  You could put something lighter in the mix after you pour it, maybe some empty bottles?

Anyway, yes, this can be done with concrete.  Concrete would be very strong, and no you don't need mesh in this setting.  The tensile strength of concrete is terrible but the compressive strength is amazing.