I've posted on this topic a few times over the years (been playing since shortly after AE was released). 2 turn cycle is all I'll play, I will also note I seem to be in the minority when discussion comes up and when I review PBEM Opponent requests.
For me it's a better game with 2 turn cycles.
Use of multiple day turns expands (significantly) the planing dimensions of the game. Especially the naval engagements.
The game has an exceptional AI component (not talking AI opponent here, the AI in use for your units at the operational and tactical level). My preference is to leverage this AI, representative of local commanders making their own decisions and reduce my ability to micromanage. Your pick of leaders at that level can help influence outcomes (which brings up another point, importance of leaders increases with multi-turn cycle), but as in real life...there's almost never a guarantee of any outcome, especially the more dicey engagements.
Additionally I think the 2 day cycle is better representation of the state of communications and control during WWII. That's important to me.
As noted above; it gives the AI (opponent) a bump up, it plans every day even in the two turn cycle (at least that has been my assumption, I have no facts to confirm but watching the turn progression display am pretty sure this is the case). If I start an AI game again I'll likely give 3 day turns a shot for this reason alone. You also get done (or to what ever point you or our PBEM opponent call done) twice as fast.
In the end it's about what you want, I push for maximum realism and getting the game closer to a simulation. For that reason I've also moved to LST's "Bottlenecks in the Pacific" Mod which builds on DBBs changes to game mechanics, expansion of forces with some additional historical elements not in either stock or DBB. (e.g. German Uboats)
You can't go wrong either way (1 day or multi-day cycles), either way it is a great game with superior depth.
Thanks for the detailed reply Kevin, would you still suggest 2 day cycles to a beginner?
Just a helpless noob passing by.