/u/The_Chieftain_WG has written several very detailed answers about the problems surrounding WW2 German armour, in particular the problems surrounding engineering and logistics. Here is a nicely concise example. Essentially, German armoured vehicles were often unnecessarily specialised, with a lack of common or interchangable parts which made regular maintenance much more difficult. They were also often poorly optimised or designed when compared to their Allied counterparts. More Tigers were famously lost to mechanical failure than enemy action, and the Panther was prone to spontaneous combustion of its ludicrously under-powered transmission. The British Army built several Panthers for testing after the war and concluded that the design was not fit for purpose.

On top of this, by the end of WW2, much German industry was in ruins and factories closed. By comparisson, nations could adopt Allied tanks which existed in far larger stockpiles, had been proven effective in combat, were as a rule far more reliable and easier to maintain, and in many cases were still in active production meaning that a regular supply of replacements and spare parts could be assured.

That said, German AFVs did see some service, particularly in the Middle East, where they were often used by Arab nations in the 1948 invasion of Israel and afterwards. Some Panther tanks were also kept as reserve units by the French army, but were demobilised as soon as the French ARL-44 programme bore fruit.