The Schengen Agreement has everything to do with transit. Someone with ILtR in the UK will still require a visa to travel to the continent, or transit through one of its airports that requires transit visas (CPH is one, AMS is another). The same is generally not the case vice versa, unless the pax is from a country that is required to have a UK visa (Commonwealth is generally not an issue as 3-month visas are granted at immigration on entry).
In Barcelona and Porto you are also required to undergo two security checks, although not with x-ray. If you travel internally (i.e. within the UK) with a connection to the continent, you are also screened twice, once for domestic security, once for security to the continent).
The US and the TSA pretty much do this based on passport. If you are from any country other than the US, especially those from Africa, Latin America, Asia (Japan excl), you will be pulled over for 'random' inspection, plus a secondary inspection at the gate (and boy, if your boarding pass was not marked by TSA, you will have an almighty rumpus at the gate).
S.