We have made the switch to the online version and it's working well for us so far. It is not the same as the desktop version. I would say that it's slightly less advanced with a few less options, however it still does what we want it to do. The QB app and the mobile version are essentially for info only. I think you can create an invoice and an estimate on your phone but you can't edit anything that you already have done. I at least as far as I have found so far.
The best feature for me is that now I don't really have to go to the office at all. I picked up a nice later printer and a new computer for my house so I can pretty much do everything from here. The upside is more time with the fam. The downside, (like I did today) working at home keeps work on your made at all times. This morning I was entering customer payments and credit card charges at 7am. What a way to spend your Sunday morning.