I find it is very easy to copy a password from KeyChain Access or 1Password onto the clipboard on my Mac then simply pasting it on my iPhone or iPad. No third party app required.
Way beyond your password functionality is the ability to type texts on a Mac and transfer them to an iPhone, but I don't know enough about iPhones to answer this question myself...
Unless there's some aspect of the phone of which I'm unaware, the handoff method you use seems to me to be preferable to the app, because with handoff you've got the original on your Mac to edit and recopy/paste, whereas with the app, there doesn't appear (to me) to be any way to edit what you've typed after you've typed it.
