indie,
I think you're probably right that there is a sense of public guilt left over from Vietnam, while the vets themselves are seemingly keen to avoid a repeat of the 'guilty homecomings' of the 60s and 70s.
I also agree that forces on both sides of the Atlantic have remained largely apolitical; the US public generally support the troops even if they object to the policy, while in the UK all parties use our forces' successes or shortages of kit to make differing political points (my personal grievance is the use of troops as a backdrop for political statements, while denying the troops themselves the right to speak freely).
The reason for the difference in 'loving its forces' is certainly tied-in with patriotism and national identity. Lager-swilling morons in the UK default to signing the national anthem and wearing the Union Jack for short-term reasons like a football match, only prolonging this behaviour as long as England remain in the tournament. The same morons almost certainly wouldn't stand upon hearing the National Anthem in anything other than a sporting environment - probably because standing would require them to go against the group mentality that urges them to chant In-ger-land on other days.
The Falklands was a classic short-term war that allowed lager-swillers to get the flags out, in between World Cups, direct their jingoism towards an identifiable group - the Argies - while shouldering a clear sense of the UK being the victim of aggression. There were few question marks over the rights or wrongs of policy, purpose etc. In short, the Falklands was quick, relatively uncomplicated, and suited our takeaway society.
The problem with Afghanistan and Iraq is they're both long-term campaigns with unclear objectives, invisible enemies and, particularly in the case of Iraq, controversial motives. Add spin and the tabloids and dilute to taste! Both theatres lack significant Iwo Jima or Falklands-style victories and resultant flag-waving imagery - while underlying religious polarity requires successes to be dealt with sensitively!
The UK generally loves its forces too, although the press swings between 'SAS Hero' and 'Drunken Squaddie Rampage' stories at will. And while Americans hang on to their underlying patriotism, the UK public would be just as bored of X-Factor if it had gone on as long as GW2 without a clear winner.