"Ex-pats" in the commonly used sense, who hop between well paid postings with significant perks (such as relocation agents and hefty international school fees paid) have a totally and utterly different experience to those who simply live outside their country of birth, sending children to the local schools and often staying longer/ permanently in one place.
I have encountered a significant group of of ex-pats of the ilk who use international school by preference (Western Europe) and socialise 95% with other ex-pats ... they are giving their children an experience, but it is a very specific experience of being an ex-pat, very specifically - skimming the surface of the countries they basically visit for a few years and look at from the outside in, largely as observers, socialising with other English speakers or perhaps very internationally minded, English speaking local colleagues, never considering doing anything other than using international schools ... usually employing "help" in the house... the air is rarefied! The children do meet people they wouldn't if they'd stayed in their parents' home country, but these people are very often simply other ex-pats, albeit from various countries, rather than the "normal" local population. It's like a very elite, socially acceptable, monied version of being a traveller :o
Other ex-pats I've met here have tried just blithely chucking their kids into local Kindergarten and school, usually for long hours "cold" from a home environment where the language isn't spoken, assuming "kids are flexible" but at the same time they constantly compare the country they live in negatively to "home", moan about everything, socialise exclusively with ex-pat friends, and make little effort to have local kids over at theirs regularly or allow their kids to do things the "local" way - and they wonder why their children struggle socially, don't pick up the language fluently, struggle at school - they blame the country and claim people or the system are "anti foreigner" (which they can be in some circumstances, but if you work it right being an English speaker gives you a free pass on that as it has perceived value).
I think its a fine line and not a done deal that by living abroad you automatically imbue your off spring with a fantastic international mindset, flexibility, confidence, ability to get on with anyone, blah, blah, blah ... you can end up with alienated, unhappy children who don't feel they belong anywhere, including when you "give up" and "go home" to a country the kids have, in fact, only visited for 2 week holidays, and don't feel at home in either. Or it can work out well. Its partly down to luck, partly down to how thoughtfully parents handle the whole thing, and partly down to what sort of children you have - arguable the thick skinned, self confident, resilient ones might have been like that anyway! :)