As a non-US and non-EU person, I can confidently say that the US has better free speech laws than anywhere else on this planet. I am open to being educated on this though.
Treating freedom of speech as completely disjoint from freedom of press is wrong.
Obviously there are exceptions, in the form of breaking contracts. Can't go around leaking classified information or industrial secrets - contracts you agreed to when you signed up for the gig.
If you can't even exercise free speech where it really matters in regards to your democracy, you hardly have total freedom of speech.
Also Snowden is hardly the only example of whistleblowers from within a branch of a democratic government speaking out. However the US is an extreme outlier in how it handled the matter.
Another thing many western democracies manage to do without is an equivalent to the US's National Security Letters, which are also a form of the government policing speech where it might matter.
So apparently you have to be afraid to speak out when it really matters, but at least you can deny the holocaust I guess.
In the USA things like defamation, incitement to riot or lawless action, speech covered by copyright, terrorist threats etc. may land you in big trouble. In the EU same thing for for example holocaust denial. And in other places, such as for example Russia, the constitution might grant you the freedom of speech, but the system enforcing the constitution does not.
It is difficult to compare countries directly because of different laws and legislative systems. The use of some form of proxy metrics like the Freedom of Press Index might be useful, but then the question becomes which metrics should be used, and when presented with several metrics, there is a danger to select only those metrics which enforce existing viewpoints.