1) Here ‘sit a horse’ refers to his general ability as a horseman, everything involved in riding, fighting on horseback and so on. So he is saying that he masters the skills involved in riding a horse, given the context, in battle, as well as anyone else. 2) Here it means that Tyrion was as familiar with the maps of that region as anyone else who knew the maps well, the implication being that he has a thorough knowledge of the maps. Generally speaking ‘as well as anyone’ means knowing something very well.

Hi; In both instances, what is being said is that there is no one better. He is equal to, or better, than anyone available. I hope this helps., Stephen

Have you ever sat on a horse? If not, you need to know that it is not as easy as it looks to follow the horse's or horseback's movements in the different gaits. In riders lingo: The rider must learn to sit "in" the horse rather than on the horse. Both bodies must "merge" into each other and become one (like a centaur). To sit a horse means as much as to sit in the horse. So the first sentence means Jon is as good a rider as anyone else. The second sentence I understand like Tyrion knew the area well but only in theory (on the map). Reality didn't match his imagination of it.