Not going to change much for the average person.
EU is a bunch of national politicians patronizing their voters first, by introducing unpopular laws and measures they couldn't possibly introduce directly.
Then it's the same national politicians patronizing each other across borders -- Greece, Italy, Spain, Britain, even Germany... everyone gets their share of being patronized against doing useful stuff, necessary for the middle and the lower class citizens.
Last but not least everyone is being patronized by Big Business, who's effectively running the EU.
If Brits succeed in exitting, then if anything, it will at least show the rest of the EU conuntries that doing things just "because EU" is not the only option. That hast at least a marginal hope of getting some useful change.
Don't get me wrong, the concept of a unified Europe is cool. But the EU is not a unified Europe, it's a patronizing institution run by business, for business. We can try this again in 20 years, properly done, startgin democratically first and economically later, not the other way round.