TITLE: Why is the simple trace formula a weaker tool than the Arthur trace formula?
QUESTION [9 upvotes]: What are some concrete examples of theorems which can be deduced from the Arthur trace formula, which do not follow from the simple trace of Kazdhan and Flicker?
(So I do not mean weaker in the sense that the Arthur trace formula implies the simple trace formula.)

REPLY [3 votes]: This is an addendum to Jason's answer. 
Mueller [1] and Lapid-Mueller [2] have exploited Arthur's trace formula to come up with a Weyl law for GL(n) with an excellent error term. (Their method has been adapted by others, Matz, Matz-Templier etc.). Since they are counting all automorphic representations (with a fixed infinitesimal character), the simple trace formula simply cannot detect them.
Much more importantly, Arthur's trace formula has been an indispensible tool in proving important (endoscopic) cases of Langlands' functoriality which hasn't been done (cannot?) by other trace formulas. We now have functoriality so far for classical groups, unitary groups, their inner twists, spin groups. 
Nevertheless, Labesse-Mueller proved a weak Weyl law and also Kottwitz could prove the Tamagawa number conjecture (see Jason's answer) using weak test functions in Arthur's trace formula. 
[1]: Mueller, Weyl's law for the cuspidal spectrum of $SL_n$
[2]: Lapid-Mueller, Spectral asymptotics for arithmetic quotients of ${\rm SL}(n,{\mathbb R})/\rm{SO}(n)$ 
[3]: Labesse-Mueller, Weak Weyl's law for congruence subgroups