When I plotted Puff's weight X her age through her first year, I used days.
Since some months can be 28, 29, 30, or 31 days long, they're obviously too crude (too variable) a measure of age for that purpose.
It really all depends on what the purpose is.
If, like me, you're making a graph to keep a record, you'll need equal intervals along the horizontal X-axis (age) -- [as well as the Y (weight/pounds)].
But when someone asks you how old your Lab is, IF you tell them "167 days" that wouldn't help much for many people. Saying "5 months" or "5½ months" is a response that most people would quickly understand.
It just all depends on the purpose.
If a medicine needs to be given 2X/day for 21 days, you use days.
If you're going to feed a Large Breed Puppy food for the first year of life, you can use years (or 12 months) and if you're a few days, or even weeks, one side or the other of 365 days, it really makes no difference.