Data Centers that are hosting websites and web hosting companies mostly use SSD drives because that's what web hosting companies and web hosting customers and website owners want their websites hosted on.
For backups though and other data centers and server farms they still use HDD drives.
As far as I know Google still uses HDD drives to host their search and other data as well as youtube videos.
In the future though all data centers may eventually use SSD instead of HDD that is if the price continues to come down on the SSD drives.