I'd love this question to be open ended, but to further clarify what I'm getting at let's say we look at Alaric's army in 410 and Charles Martell's in 732. How different are these armies? Have any major innovations been made in the 300 yeas between the two?
u/Alriclofgar has an excellent, elaborate series of posts on a very closely related question here:
The answers, obviously, are mostly concerned with the material aspects of spear and shield construction (which are easier to answer via the archaeological record anyway) but Alric also describes the tactics that these weapons would have been suited for.
I've linked the entire thread rather than the specific posts because there is a lot more fascinating material there, including an extensive discussion on the nature of the Anglo-Saxon invasion, or rather if there even was one, and the meaning of the early-medieval written sources from Britain. (Gildas et. al.)
Follow up question:
Why was the quite successful Roman testudo formation not longer used in Western Europe?