You know, I don't think the majority of migrants who set off on a life threatening journey, having paid all of their life savings are thinking much about benefits.
I think they are thinking more about the "push" factors (like being beheaded, starving, being tortured, their children being killed etc) than the "pull" factors like oooh....not being allowed to work, living on as little as £5 per a day, going through a stringent process, being hated by their new community and all the other toptastic things like that.
Aside from the fact they not getting horribly killed is probably the number one factor in getting on that boat, these people pay a lot of money to make that journey. Which means, that in their home country they were somebody, had a good job, a career. Which maybe they liked. Maybe they hate the idea of never being a doctor, insurance broker, small business owner again. Maybe living on handouts is an awful thought to them (but it's the living bit again that's motivating.)
Also - I bet in places like Syria there aren't loads of programmes on TV about how awesome the benefits are in Europe and which country should you choose. They probably have very little awareness of the benefits systems of other countries. Have a think about it. How would they be likely to have all this knowledge about benefits? Maybe they pause in between the fleeing and not getting killed for a good chat about it, or maybe if you got the Somalian version of the TV Times it's back to back with shows about European benefits and how to claim them. But I doubt it somehow.
Anyway. Thank God some of them make it here and end up safe. Thank God some of them are able to rebuild their lives and contribute to our society. It's a shame it's not more.