I don't quite understand why one is better than the other. Even the best moves that follow I don't understand. Can anyone clarify? Thank you!
It looks like it comes down to activity. With Ke2, black gets a lot more activity and white's king ends up out in the open.
Yes, it is activity, but more to the point is this: I think with the King on e2, White does not have the ability to let the Queen retreat to e2 with check if Black tries to immediately play Nf6. For example: 1. Kd1 Nf6 2. Qe2+ and now the check must be addressed and meanwhile the Bishop on f2 is threatened, and the Rook on h8 is threatened. It appears that after 1. Kd1 Qg5, this is Black's best "try", but after the exchange sequence White is up a full Rook and it will be very difficult to get the Knight on h8 even though it looks helpless at the moment. Even if Black does get the Knight, chances are Black will still remain down the exchange and with the position pretty open, the Rooks will be powerful.
I don't quite understand why one is better than the other. Even the best moves that follow I don't understand. Can anyone clarify? Thank you!