Eh, lots of different fine points, but they do share something of a common starting point.
Really, for any given area (city/county/state) you need to check up on the various laws (last I saw, there was still an old law against eating ice cream on Sundays...) in your area. But no matter what, it's not a good idea to flip off police officers.
UK does not have a constitutional system, also the court system is far less adversarial. in any case, the main difference is that the 1st amendment applies solely to the US. many european states are fine with criminalizing offensive speech (denial of holocaust, for example). anyway, you dont seem to realize that the 1st amendment was incorporated (look up incorporation) to the states in 1925 and no state or local law will ever take precedence over it. any reasonable lawyer would have no problem proving this is bs.
even if it is a law, that doesnt mean its enforceable. especially a local or state law when it conflicts with free speech. the courts declare laws unconstitutional all the time. in the UK, the courts do not have this power, showcasing yet another major difference between the two systems. you are wrong and should not spread misinformation. if only more people knew their legal rights, the police would do a whole lot less damage.