AT = Anti Tank
TD = Tank Destroyer

Well, first of all, ATs are in the unarmored armor class, and TDs are in the heavy armor class, so units will treat the two types differently(units will have different attack values and defense values against each). If you are short on oil, ATs are the way to go. It does not require oil, but TDs do. TDs have slightly higher attack and defense values against tanks. ATs have slightly shorter production times. They both receive strength boosts in mountains and cities. It depends on the circumstances, so choose wisely!

Also, TDs are fast moving units, and ATs are pretty slow.

another thing is, anti tank is hidden in urban and tank destroyer is hidden in forest. They are ambush units on their respective places. yes they are doctrine thing too.