Emissions and fuel economy go hand in hand, except for NOx. Diesel makes more NOx and soot. I've heard some people say that their clean diesel tail pipes are cleaner than one on most gasoline engines though, because there's no soot collection on a gas model.
When we were engineers in the 70s, we did a survey of fuel economy on our cars and trucks. We had about an equal # of diesels and gas models. The gas models (all with carburetors back then) ran 30 mpg-ton. In other words, a one ton car (and most economy models were almost exactly that back then) would get 30 mpg. The diesel correlated @ 45 mpg-ton. No turbo engines.
In the meantime, turbo charging and fuel injections have come along. In my rough estimate from observation of mpg changes with these, fuel injection generally will improve fuel mileage by around 20-25%. Turbo charging is good for another roughly 25%. So, you can easily see where a fuel injected, turbo-charged gasoline model will almost make that 50% gap we observed. Throw in computer control (e.g. shutting off fuel when coasting, etc.), hydro fans and electro mechanical steering in place of power steering pump, and you can easily see how gasoline-engine vehicles will get probably better mileage than a plain diesel engine. Put turbo on the diesel with the same goodies, and it'll be 20% better IF it doesn't lose anything via diesel regens on the exhaust system. Unfortunately, the diesel regens (usually done with a tiny bit of fuel injection increase to start the burn) go a long way to killing that 20% advantage. A typical high mpg diesel car (like a Cruze TD or VW Jetta TDI) with urea injection will do 46 mpg average. The equivalent gasoline model with turbo will do 39-41.
In actual testing, one tester showed about 49 mpg on a Jetta TDI on the hwy while a Mazda3 did 47. The Mazda3 is about 200 # lighter than a Jetta though, about the same as a Golf.
Ralph