But all those rights in the US are only guaranteed subject to the make-up of that Supreme Court. They get to decide what that Constitution means. There are vast numbers of ways 'fee speech' is restricted in the US, even more so in the past.
Either way, with-or-without a written constitution, the ultimate 'guarentee' is just 'what the populace will tolerate'.
Free speech is subject to a few exceptions: child porn, civil liability (not criminal) for defamation, under a heightened Constitutional standard requiring malice (not required in the UK), a very limited exception for incitement speech, false advertisement (again narrowly defined and rarely applied) and, used to be obscenities, but now all porn not involving children is de facto legal. There is nothing new of which I'm aware.
Yes, scope of the 1A is subject to the interpretation of SCOTUS, particularly around the margins and in the gray areas. Yet we haven't had anything remotely resembling the Alien and Sedition Act since 1803.
By contrast, in the UK, they could pass the Alien and Sedition Act tomorrow and it would be perfectly legal. Oh wait, it's already illegal to imagine a world in which your monarch is not your monarch. Literally, there is an active law on your books which makes it a crime to say, "wouldn't it be great if the UK had no monarch?"
en.wikipedia.org
Edit: my apologies, the UK did finally repeal that in 2013. Phew. Let's hope they don't decide to reinstate it by majority rule tomorrow.
We can compare and contrast the two systems in various theoretical ways, but the result of the difference is that free speech is narrower in the UK and on the continent than it is in the US. The list of exceptions is too long to bother with an extensive discussion.
en.wikipedia.org