Most importantly: don't push, don't evangelize. Be absolutely sure about your motivation. If there is even a hint of missionary work, don't start. The overwhelming majority of people react either annoyed or aggressive, because the mere suggestion to check out another workflow carries an undercurrent of criticism. That your workflow may be better than theirs. Which closes many people off. Actually, this is a general principle that works regardless of setting (think Vegetarians/Meat eaters, Democrats/Republicans, car brands, recipes, …) They all do what they do because they believe what they do is the right way to do it.

It may very well be that no criticism from your side is intended in the first place, but this happens on the other side and there's nothing you can do about it. That's humans for you.

I suggest bringing the subject up when there is no deadline, in a relaxed setting. Talk from your experience, in a way how impressed you were and how much more efficient you feel now. Never compare. Never say "it's better", as that would be an absolute statement, just asking to be challenged. Always go with "I'm more productive this way". This way the other person cannot dismiss that you may indeed be more productive and you don't apply any pressure. If the other picks the topic up, be gentle and maybe offer to share a link or two, Vimcasts is a great resource for example.

Learning Vim is a hell of a task, especially considering the insane amount of time you invest to get your very first setup right. I had so many question marks in my head during that time and about every second setting seemed nonsensical or even hostile. It's the opposite of intuitive. Either someone sticks with it and gets progressively more "aha!" moments or will just drop it for a more Word-like editor. Whatever works.

In the end it's really not worth any debate: everybody just uses what gets the job done. That's the beauty of source code: it's universal.