It uses a random dice generator for rolling, so one can argue that the luck is the same. Playing online allows you to have a larger pool of people to play with and to play on a map without having to worry about setting it up. With a larger pool of people to play with, I can say for certain that I learned a lot of new and neat strategies that helped me become a much stronger player.
The game usually records one’s moves in a ‘game history’ so that you can remember what you did and you can easily undo your moves. Once you finished deciding, you press a button to move onto the next phase. If you are familiar with the late 90’s A&A cd-rom, its kind of like that. (Specifically, I am speaking of TripleA).
Probably the best part about it is you can save the game for a later time and reload it when you get with your opponent again. It gets better when you have a group of people you know actually schedule a time to meet online to play against each other which can be more convenient than going over to each other’s houses sometime.
You can also send saved games between one another if you wanted to do a ‘Play by Email’ or ‘Play by Forum’. This allows you to post important parts of the turn (die rolls, moves, etc) on the forum or an email so you can play anytime that you yourself feels like it is most convenient, albeit it takes longer to finish. The dice rolls are emailed right when someone else rolls and with the history, it is almost impossible to cheat without someone else noticing.
When you get the time, check out TripleA. I always like seeing new players who bring original ideas to the table.