I am curious why in the solo version monsters gain a base of 3 power while in the 2 player mode, they only gain a base of 2.
I would think that this is because there is an inherent advantage to the different turn sequence and/or maintaining a single deck instead of two (other than reducing shuffling).
I don't know about turn sequence, but I feel that maintaining two separate decks is an advantage over maintaining a combined deck. With multiple decks, you can (and should) specialize your decks. With a single deck, this doesn't work. In my recent plays I was often hampered by drawing several (good) actions in one hand and only none in the other. Not only where the monsters coming out more rapidly than in a two player game, but my deck was slower...
The primary advantage is the pace at which your deck can improve relative to how quickly the monsters act. Consider the Seal: In a 2-player game, if a Shadowrift comes out on turn 1, it provides power for at least 2 turns. In a 1-player game you could buy a Seal and a Prophecy and seal that bugger the next round.
This advantage can turn against you if you let yourself get too banged up, but that's in line with the advantages and disadvantages of working solo, innit?