This list certainly isn't all inclusive (and in no particular order). I'll just list Pros of both as most of the pros of one are cons for the other.
Offline:
- Can change opponents' uniforms (it sucks playing teams like Oregon every year and only seeing the same 2 uniforms every season).
- No need to be connected to internet (IE. can still play when internet is down)
- Many fewer dynasty specific bugs (ODs have some really nasty ones)
- Far fewer game losses (not loss like win/loss, but loss as in results gone and you have to replay the game) due to stupid stuff like highlights not loading or freezing
- Can edit all coaches (which I'm pretty sure you can't do in an OD, but maybe the commish can). This is huge for things like making normal no huddle coaches into aggressive no huddlers as an example
- Can edit every player in the dynasty (in '13 OD player edits didn't stick, but I don't know if this is the case with '14). This is huge for things like when teams like Oregon or Georgia Tech recruit pocket passers, you can make them into scramblers so they can run their offense properly.
- Can have multiple saves. I have a save at the end of every season so I can go back anytime I want and see stats or records or polls or whatever from any season.
- Can play/sim games not involving your team. This is nice if you just wanna play other games or if you wanna prevent a ******** upset (if Alabama loses to FCS, I'll supersim the game to prevent that from happening).
- No need to worry about EA servers being unavailable (when they're unavailable, you can't upload your OD game).
- Advances are MUCH faster than with OD.
- You can control up to 12 teams if you want (with 12 different coaches) whereas in OD you can only control 1.
Online:
- Dynasty wire is really awesome. Not only are some of its things better than on the console (IE. it's standings page), but you can view it anywhere, anytime.
- You can write stories for the wire.
- Recruiting from the web.
- If you pay for it, you can advance from the web as well. (End of season? advance all the way to the preseason and setup your recruiting board in preseason while at work).
I know I'm missing some stuff, but that's at least some of it. I will say that the number of OD specific bugs is quite higher than for offline dynasties (but some of these seem to be specific to non-commishes, so those wouldn't affect a 1 player OD, but there are still some that would). ODs are amazing with 11 other guys (and I've been in the same one for 4 years now), but I personally would never play a 1 person OD as I find the offline version immensely superior.