When it comes to IPv4, CIDR notation is just a different way to represent a netmask. There is no difference in the netmask presented in any of the following ways (i.e. it is the same netmask):
Dotted decimal notation: 255.255.255.0
CIDR notation: /24
Binary notation: 11111111.11111111.11111111.00000000
Hex notation: ff.ff.ff.00
In your own documentation and design work, you can use any kind of notation you like, however keep in mind that if you use anything besides the first three, it will likely not be understood by anyone else. The first two are common, the third you normally only see in training/education and I only saw the last once long ago when working with a developer that preferred to work in hex.
As for support in device configurations, you will generally only see support for one (or possibly both) of the first two.
With IPv6, nearly everything will use CIDR notation, although I have seen (one time, although it makes little sense) someone use hex notation for the mask as well.
What can we do using CIDR that we can't do using netmasks?
Again, to be entirely clear, CIDR notation is just a different way to represent a netmask. What can we do with CIDR notation that we can't do with dotted decimal notation?
Represent the netmask with as little as two characters. It is simply easier and shorter to either type or write.