Reading up on the positions and titles of the two men it seems they are entirely similar:
So what qualifies Octavius as an emperor but not Caesar? It seems to me that either both should be classed as such or neither should.
Your answer is in this thread here.
My reply to a similar question has kindly been linked already. Please do read it as it addresses the meat of the issue.
I would like to respond to a few of your points specifically.
Firstly, perhaps both tried to nominally maintain the image of a republic, but in Caesar's case it was a lot more obvious that he was concentrating all power in his person. Octavian steered clear of the whole 'dictator for life (for no reason)' thing.
Secondly, regarding the absolute rule, Octavian had wiped out his enemies a lot more thoroughly than Caesar had. By the time Octavian became Augustus, he was in a lot more secure position than Caesar ever was.
Thirdly, the title of imperator was nothing special really. At this time it just meant someone was a victorious general and was honoured by his own troops. Yes, our word 'emperor' is derived from the word 'imperator', but it were Octavian's other titles, Augustus and Princeps, which made him so special (compared to Caesar, who just did what others had done before him - as I mentioned in my reply linked above).