In this way I only need to alter styles which need to alter as the screen size grows.
I see this as an extension of the cascade so styles flow up the screen sizes until over-written with something more specific – i.e. based on a relevant media query.
But – if I have a style which I only want for the smallest screen size for example then I will limit it with a max-width query but I never use min-width= & max-width= type queries – I’ve never found I needed them.
I don’t think any one approach is “better” though – it is up to you which you find easiest to work with.