Yes he did get cocky, wich is a result of the so called "Imperial Arrogance" you mentioned before, but what I don't get is that he was stupid it enough to even ignore Vaders direct orders, and doubting his authorithy (the probe droid incident) There is a smal time gap between ANH and ESB but watching to the movie and noticing some details (like the completly terrified look in the bridge personnel as Vader walks by) I can make up that it is not wise too even raise your voice against Vader. And about the cocky stuff, Ozzel deserved to die, His failure to obey to the direct orders of Vader didn't only result in the great losses on the Imperial side but also made the Rebels prepared for evacuation and in a way to the destruction of the 2nd Death Star. (Because of Ozzels Ignorance the Rebels escaped could form a new base, gather enough forces and even take the Empire head-on, if Ozzel didn't came out of Hyperspace to early, the Imperials would have bombarded the planet, destroying the base for the biggest part, and disabling the Ion cannon wich made it possible to capture all fleeing rebel ships because those transports only got away because they disabled the first wave of Stardestroyers)