I think the driving force for a leave vote anywhere, just like in the UK would be immigration mostly (ironically perhaps mostly non EU immigration fear, which is hardly a EU matter) and pure populism in the form of "we don't want to be governed from Brussels". The question is just if the fear of the (economic) consequences outweigh it. I fear that voters of several EU countries would accept severe economic consequences, or at least the risk thereof, because immigration or because Brussels.

Italy won't vote out because of a "better deal outside" (nor do I believe the UK did!). They'll vote out if populists can convince them there will be fewer immigrants without disastrous economic consequences.