The UX (and design) of 1Password is way better.
But another important reason is that LastPass is a central service where you have to (at least somewhat) trust them to not screw up since all your (encrypted) passwords are on their servers. With 1Password there is no such mandatory central service.
I'd say the only reason to use LastPass is if you're cheap, or if password-sharing is a daily exercise for you.
The Android app is read-only. It gives you read-only access to your 1Password database in Dropbox, but that's it. It works, but they really need to give it some love and bring it up to par with the iOS version.
Guh? I've got KeePass+DropBox on my Linux laptop, iMac desktop, Windows 7 work desktop, and Android phone. What's missing?
I'm sure it is possible to get KeePass working smoothly but I'm also happy to have paid for what feels like a better solution to me.