1. Accessing 1password.com's from a browser is less secure than using an app. You can choose never to log in but it makes it harder to recommend 1Password to journalists, political dissenters, etc. The most paranoid people need a local vault option.
2. The 1password.com can change to work differently from Dropbox at any time. 1Password for teams already allows recovery without your master password. They can add this to the normal subscription at any time.
The other major concern would be that you are moving your trust in the security of your data from very large companies that have staff in place to maintain such security as well as an established track record of offering service in the wild to a much smaller company with much less of a track record.
I understand this argument for iCloud, but Dropbox does not have a history of strong security [0] [1] [2]. This doesn't mean that AgileBits is more trustworthy, but it makes sense that they'd prefer to build their own cloud service over relying on Dropbox for the security of their customers' data.
1. Accessing 1password.com's from a browser is less secure than using an app. You can choose never to log in but it makes it harder to recommend 1Password to journalists, political dissenters, etc. The most paranoid people need a local vault option.
2. The 1password.com can change to work differently from Dropbox at any time. 1Password for teams already allows recovery without your master password. They can add this to the normal subscription at any time.