I have noticed that older tefillin — those manufactured a while ago — are typically shiny, whereas newer ones are typically matte. Is there any reason for this?
There is no halachic or customary reason for the change in paint styles. The following does not entirely answer your question but is relevant:
It used to be common for cheaper peshutim to be painted with a very stiff black putty (tiach in rabbinic Hebrew). Depending on a couple halachic factors, this is either kosher or not on a case by case basis but that is what was used and that putty happens to be very shiny. Gassos are made with many hiddurim that were much harder to incorporate with older technology and are painted with a thinner putty that doesn't do anything structural at all.
I don't know if this was done intentionally or not, but a matte finish is a fairly reliable indicator that the sofer does not have to check for tiach.