Well they were both in the top 5 list of Emperors, although as you say Trajan at 3rd just had the edge on Hadrian who was 4th.
In a nutshell, if you compare the two, Trajan was all about expanding the empire and conquering new lands and peoples, which in itself led to size issues in that the vastness of the empire became difficult to manage. Hadrian on the other hand (who succeeded Trajan) decided to contract and consolidate, preferring to close borders (some big wall somewhere!) and defend. Trajan was a military man and believed in warfare, whilst although Hadrian was also a military man he was very fond of the arts and poetry. Ancient Romans weren�t greatly fond of an arty-farty emperor who didn�t really spend a lot of time in Rome during his reign and was also a known homosexual (Antinous was his lover), Romans preferred an ambitious emperor that would keep rule for the people and bring them wealth and power through the might of Rome.
Hadrian was unpopular when he ascended to become emperor. Immediately Hadrian alienated the senate because of the way that they had handled a past conspiracy against him. In this conspiracy, four ex-senators had plotted treason and were consequently executed by the time Hadrian became emperor. Hadrian denied those accusations but he was still relatively unpopular with the people and so set out to repair his reputation through conquest (Parthian Triumph).
It is thought that the death of his lover made him go insane in his later years and turned him into an old tyrant. This the senate despised and he died an unpopular man. The senate even refused to deify him as is typical with emperors, but with the intervention of his successor Antonius was this finally granted.