The best storage for fixed brains is -20C in cryoprotectant. It will best preserve protein structure for future histology. If you fixed them to preserve mRNA for later measurement then consider 30% sucrose infiltration followed by long term -80 storage.
A definitive answer depends on your use but PBS with azide for long-term storage is not typical and likely there is a reason for that.
We have good experience with storing pre-fixed brains in PBS with sodium azide for later use in histochemistry. We keep them in the fridge. It is better to keep them uncut rather than to keep the cut sectionsin -20, especially because the sections get more and more prone to damage by antigen retrival methods (e.g. proteinase K). For biochemistry I recommend to snap freeze them without fixation and to keep them depending on what you want to look at at -20 oder -80.
You did not say what you would use this tissue for. If you have any wish to use it for EM, better save some samples embedded-- as the membranes etc will be degraded. If you have -80 storage (see comments above) cryoprotection storage is the best all round method. For immunocytochemistry and many special stains you can store it in the refrigerator (I had monkey brains in the refrigerator for 10 years and was still able to stain for enzymes and neurotransmitters. But if you wish to quantify such things different storage methods must be used. See above , snap freeze). If during your storage the pH and osmolality is off, things like mitochondria will not be optimal. So if you are not thinking EM but may be confocal, you may have an issue. Good luck