In my anecdotal experience on the Internet I see the x-system vastly more often than the h-system. It has the major advantage that there is less ambiguity so it is easier to automatically convert away from it. If an automatic system is used with the h-system it would need to have special exceptions to cope with words like flughaveno.

However the h-system is the one officially backed by Zamenhof which gives it a lot of weight. I have a feeling the h-system is more common amongst people who learnt Esperanto before the Internet age because in that case the automatic conversion was less of an issue.

Some evidence can be gathered with a quick search on Telegram for the following words:

manĝas: 170 results mangxas: 35 results manghas: 0 results

However it's worth stressing that in this day and age there are very few situations where it is not possible to type the letters correctly and using either system just appears lazy and inconsiderate of the reader. Even if someone doesn't want to take the time to find a suitable way to type the letters on their system it is still reasonably easy to convert the text using a webpage such as this one before posting it.