It would definitely be the Middle-Ages man, since the Anglo-Saxon times person just sounds like a stock hero from a normal written epic. Well, to be fair, they both do in my opinion.
I would select the Middle-Ages man, due to many different factors at play with him. He has a strong sense of justice, and was very well-versed in science, poetry, and the arts, meaning that he was well-educated and read some on his down-time, meaning that he would know what is going on during this time period, and would be quite caught up and understanding of what is going around him.
The Anglo-Saxon man just sounds like a warrior who was a war hero, but not much for books. I imagine Andrew Jackson, but without any intellect if that's the case; I would heavily dislike that "warrior."