If I plan on taking an international trip early next year (several months from now) but my passport is expiring in a couple months, is there any benefit in renewing it before it expires versus waiting a couple more months? No idea if those extra few months 10 years from now would be of use, but all things equal, might as well.
Each country has different rules regarding passport renewal, and the process normally depends on how recently your passport has expired. eg, if your passport has expired less than 2 years ago you may be able to do a simple "renewal", but if it's more than that then you might have to do a full new application. I would suggest checking with your countries passport office to determine if there is a difference, and how long past the expiry date the change in process occurs.
Otherwise the only real reason for renewing early is that it means that you have a valid passport in your hands. If you have an urgent need to travel for some reason, and your passport has expired (or even, depending on the country you're travelling to, if it has less than 6 months validity remaining) then you will not be able to travel.
If you have renewed it before the 6 month mark, then you're ready to travel at any time if the need arises. If you know that you're not likely to need to travel internationally, then you can hold off until closer to your planned trip.