I'm looking for things like armor, weapons, siege tactics, formations, and overall combat effectiveness. Would the quality of an individual/s training have increased or decreased? Were the Roman generals more talented during the Republic or the Empire?
I don't think you're getting any answers here because Roman history lasts hundreds and hundreds of years. The Romans changed their tactics very often depending on the enemies they faced or the manner of a defeat. You'll have to really narrow down your question to get an answer that isn't a lengthy essay or book.
Of which eras are you speaking?