Why does ammonium carbonate smell?
There are two reasons.


As mentioned by Ivan Neretin in the comments, carbonate is the conjugate base of a much weaker acid than chloride is the conjugate base of.  In other words, carbonic acid is less acidic than hydrochloric acid, and carbonate is more basic than chloride.  This means that carbonate solutions will have higher pHs than chloride solutions, in general.  At higher pH, the equilibrium between $\ce{NH4^{+}}$ and $\ce{NH3}$ is shifted more towards $\ce{NH3}$, which is volatile and smelly.  
Carbonate is also potentially volatile.  If you leave ammonium carbonate, even in solution, around forever in an open container, it will eventually completely disappear.
$$\ce{(NH4)2CO3(s) -&gt; H2O(g) + 2 NH3(g) + 2CO2(g) }$$This also favors more vaporization of ammonia.  In contrast, in ammonium chloride, chloride is essentially completely non-volatile.  Thus ammonium could not evaporate without a buildup of negative charge in the solution, highly unfavorable.