Which is better for constructing buildings and large-scale terrain pieces?
Generally, Foamcore is thicker and better for doing the general shape of the building, while plasticard is better for the finer details.
If you're doing small buildings, you could do them entirely from plasticard. I've seen an Imperial Bastion made entirely out of card stock and it holds up well. Plasticard would be even better for such things.
Which is better for creating scratch built titans and conversions?
Again, I'd say foamcore for the big parts and plasticard for details, if you want to put fine details into the conversion. As someone said above, some of the structural elements of a titan are better done with plumbing and PVC.
Is there anything that might cause either material to melt, (like polystyrene and spray-paint)?
For Plasticard, anything that would cause plastic models to melt will likely cause plasticard to melt. So, model glues, strong solvent, etc.
For Foamcore, the outside is paper and won't melt, but the inside is still foam. I'd try to avoid spray-paints and acetone (nail polish remover).
There are some spray paints that work well with foam. In the US, Krylon has a line of paints known as "H2O" that are water based. They take longer to dry, but they won't melt foam.
What painting techniques work best with either material?
Personally, I use cheap craft paints for terrain. You'll go broke trying to buy
GW paints for anything large.
Otherwise, same techniques as small things. Just make your techniques bigger.
What glues create the best bonds with either material?
For foamcore, you want to use PVA glue (white glue). In the US, Elmer's and Aline's Tacky Glue work well. I'd avoid super-glue because it will melt foam. Plastic cement will also melt foam.
For plasicard, PVA works. Super-glue works well, also. Plastic cement is best for a long-lasting bond, but it may cause a bit of melting/bending where you don't want it.
Another note,
If you're looking for materials for basing your terrain, I'd avoid foamcore. If you glue anything to it (sand/flock), it will warp and curl and it takes a good amount of force to straighten it again. For that, I'd use
MDF board.