The word "privilege" is one that I use with extreme caution in any context but especially when talking about migration. C. Lundström wrote an entire book about White Migration in which she argues that race is part of that Invisible Knapsack and it travels well.
My thinking about "privilege" is evolving and by that I mean that I haven't come to any conclusions that satisfy me and I'm open to more information. I'm also very wary of my own feelings and visceral reactions. A part of me would very much like to be seen as "privileged" and bask in the notion that I am a special snowflake. Behold the wonderfulness of me! The saner part of me says, "Hey, kiddo, get real." (And I can't tell you how many AA meetings it took to get that one straight in my head.)
I'd say that "privilege" has so many negative connotations, is so relative, and so muddy that I prefer to reframe it and use Bourdieu's idea of "social capital" instead. This terms captures what people are getting at when they use "privilege" but without evoking knee-jerk reactions. To make it even clearer in my head I think of it as a poker hand. Some people are born in a particular cultural, social and economic context with a lot of good cards (inherited social capital) which enables them to more easily accumulate other cards. Some folks start with really bad ones and they struggle. In between the two is a continuum where people hold mixed hands.
A good example of a card is citizenship. In The Birthright Lottery: Citizenship and Global Inequality by Ayelet Schachar she argues that birthright citizenship in a developed country is an inherited privilege that is undemocratic and unfair. It persists, however, because it's a privilege of birth that benefits just about everyone within an affluent nation-state. The poorest factory worker in France is automatically part of an exclusive club just by virtue of being born in France and having parents who were born or naturalized in France. He/she will automatically transfer that membership to her children.
It is, as Schachar says, "The quintessential inherited entitlement of our time." This matters she says because there are wide disparities in income, health, education and opportunity between the citizens of a developed country versus a developing one. So it's definitely better to be born a French citizen as opposed to being born as a citizen of Mali. In fact it may determine whether you live or die as an infant. France has an infant mortality rate of 3.3 deaths/1,000 live births versus Mali which has 100 deaths/1,000 live births. (All figures are from the CIA Factbook.) And let's be clear about this - none of us had any choice about where we were born and the laws under which our citizenship was ascribed to us.
But that's just one card, albeit a pretty important one. We are born into families, We are born into groups. We are born into hierarchies. Our social capital or lack thereof is always a matter of context and I would argue that it's a combination of cards (inherited or accumulated) that determines our relative position within a particular society. And it would be idiotic of me to argue that these things don't make a difference in terms of opportunities. However, I would be extremely cautious about taking a national conversation about things like race, class, educational attainment, language, or sex and making broader claims about other societies or all societies.
Because I would contend that the cards a migrant brings to a new country can't be played in the same way in a new context. Not only does the migrant not have the same rights as a citizen but he will be inserted into at least two hierarchies: one that positions the migrant relative to other migrants (more desirable versus less desirable) and another that places her below the native-born citizen who has an inherited position in society.
But other cards come into play here like education, skills, language, finances, race and gender. But they don't necessarily have the same meaning in the new country. Polytechnique is a big name in France and it confers enormous social capital. Outside of France? Not so much. But the degree itself may count for a lot. Money may buy a very nice standard of living in one country but go to London or Vancouver and learn how little one has in a place with a very high cost of living. Or conversely, one can move to a country where even a small amount of money means a much better standard of living. English-speakers may believe the hype about it being a highly-valued "global language" and arrive in a country to find very few jobs for the monolingual. And yet, they may find one and be very content.
As for race there are enormous variations in how it is defined locally. People who are considered to be (and consider themselves) "black" in the US , might not be in parts of South America. I don't see that Poles in the UK get to be "white" in the same way as British "whites". I have read arguments that say that being "white" is a always a good card wherever you are in the world. Honestly, I think this one collapses under the impossibility of defining racial categories when there is no globally agreed upon definition of any of them.
What I am arguing for here is that if we are going to look at people's poker hands (social capital) when they migrate, I do not think it is sufficient to look at one card and pronounce a verdict of "privileged" or "underprivileged." That's just laziness. It's simply too easy to say "these people all have at least a BA, therefore they are privileged" or "those people migrated, therefore they are privileged (or underprivileged)." (The latter can go either way.) I think that you need a lot more than that to support an argument for or against. And if this is a serious exercise you have to be open to contradictory information and willing to dig into the context,.
Perhapsa better response to someone who shouts "privilege" in your face is for both of you to gently place all your cards on the table and start asking and taking questions. What it is about my cards that makes you think that I have an unfair advantage over you? What is it about your cards that leads you to think that the deck is stacked against you? And then no cross talk, no interrupting. This is called a conversation and it can be quite enlightening when both parties are active listeners.