Caesar was appointed to the position of Flamen Dialis or the high priest of Jupiter. It was an extremely high office and one which commanded a great deal of respect. Being the flamen came with a number of perks. If you were to analogise it to the modern day, you were at the top of the Roman order of precedence. The office of Flamen came with the right to a seat in the senate, the right to wear the toga praetexta (a white toga which a broad purple stripe signifying either a high magistracy or membership of a priesthood) and the right to a single lictor. The only person who clearly outranked the Flamen in religious terms was the Rex Sacrorum who filled in for the (absent for 500 years by this time) king at some religious events. So while the office was one of great ceremonial and religious importance, it was not a politically important one in the sense that it conferred direct power and influence on the holder.
The office also came with many (sometimes kinda batty) restrictions which historians argue represent vestiges of Indo-European religion. The cumulative effect was to really hinder the Flamen’s ability to live a normal life. A full list was provided by Aulus Gellius but I will give some of them here
Now as for what Caesar thought about this we have no information. However, one thing to bear in mind is that he may, actually, have been quite pleased in retrospect. This was because of some of the other restrictions on the Flamen, namely:
The combined effect was that it would have been impossible for Caesar, had he remained Flamen to climb the greasy pole of Roman politics. The prohibition on travel would have made it impossible for him to serve as any of the required foreign appointments – for instance as a Pro-Quaestor or Pro-Praetor. It also made an appointment in the army impossible. Therefore, even if Caesar regretted being stripped of his priesthood, as a young ambitious man it saved his career.