They are like but also not like.
Shippey goes into this topic so it's worth getting hold of his books. One of the major differences is that the Rohirrim are great equestrians but he Anglo-Saxons were not. They revered horses, but they were not known for their skills in riding or driving them, unlike the Celts who were. I think that Tolkien naturally loved early English and loved the literature which it threw up and then went on to create an idealised view of the Anglo-Saxons with other influences thrown into the cultural mix.
For one, the Anglo-Saxons were by no means an ideal people as they practised apartheid, however maybe the Rohirrim also did this? There is obvious evidence in LotR that they had slaughtered the indigenous Woses, and it seems they may have also tried expansionism into the lands of the Dunlendings. Why, they even rename them! They are the Enedwaith, whereas Dunlendings is a Rohirric imposition.
So, a bit of reality brought into the mix there? I just love how Tolkien gives all his races these darkened histories and makes them less perfect. Sometimes it feels like he was a kind of iconoclast against his own creations.
