What cooking/grilling applications are more suitable for smokers than standard BBQ's?
While it would be helpful to know:


What kind of grill you currently have.
What kind of smoker you're talking about acquiring.


I think I can still give you some decent feedback.  Generally speaking, a smoker is better suited for cooking foods for a long time at a low temperature -- which is the traditional definition of "barbecue" in America -- than a grill would be. Conversely, a grill is better suited than a smoker for cooking foods at high temperatures over high, direct heat.  This is not to say you can't cook on indirect heat using a grill, nor is it to say that some smokers can't be adapted for grilling. It's just which is the more suitable tool for what job.

For barbecue, a smoker offers the advantages of better heat control at lower temperatures, and greater food capacity in the cooking chamber.

I would suggest that if you want to do a lot of barbecue, particularly things that require really long cooking times (a pork butt or brisket can go as long as 14 hours), it would be worthwhile to get a smoker.  If not, it would make more sense to adapt your grill for barbecue on the occasions that you would need it.  Actually, I'd recommend you do that first, anyway, to see if you like doing that kind of cooking. An entry-level Weber smoker can run you $300, and I would not recommend going on the cheap with your smoker.  The ones on the low end of the market do not work very well, and they will sour you on the concept.