There is no shortcode of [vimeo] by default, so presumably you're using Jetpack or some other plugin which adds that shortcode.
For Vimeo in particular, it's supported as an oembed provider in the core code. So yes, you can do just this:
And it will work fine.
However, whether it works in Firefox or not is not a matter of the shortcode, but a matter of Vimeo and Firefox and what Firefox extensions you're running and such.
Long story short, using the
[embed] code is generally more compatible because that means that you're using the current code from Vimeo itself, which would naturally strive for maximum compatibility. With an added on code from a plugin like
[vimeo], there's no telling what the heck it's doing. Use [embed]. Then at least people will be able to help you. :)