A lot of the higher fuel efficiency quoted for diesels comes not from the absolute efficiency(which is higher, but not dramatically so) but rather that the energy density of diesel fuel is higher. It's similar to phenomena like seeing lower gas mileage in a gasoline engine with winter blend gas as opposed to summer blends. Winter blends are more volatile, and in petroleum chemistry higher volatility usually means shorter hydrocarbon chains and lower energy density. Also, if you have a flex fuel vehicle, look at the mileage hit you get on E85 vs. E10.
As far as emissions go-since the US has really started cracking down on exhaust gases NOx, SOx, and VOCs have been the big focus. With closed loop fuel injection VOCs are pretty easy to control(and also helps gas mileage since the gas is actually burning in the cylinder and not coming out the tailpipe). Even without fuel injection, the solutions were usually to run the car lean, advance the spark aggressively, and sometimes run an air injection system into the exhaust to help burn anything in the tail pipe that wasn't burned in the engine. Gasoline tends to be low enough in sulfur that SOx really isn't an issue. Higher combustion temperatures tend to promote NOx formation, so the immediate solution was to lower compression-something you can't really do with diesel and still have a reliable engine. Now, catalytic converters scavenge VOCs and can also handle NOx to the point where we're now seeing high CR engines return.
By contrast, it's hard to tweak combustion conditions in a diesel to cut out VOCs, which is a lot of the reason why they(historically) have had such a distinctive smell. The high CRs inherent in a diesel(again something you can't change too much) make NOx formation a real problem and the higher sulfur content of diesel fuel tends to promote SOx formation. Urea injection cuts down a lot of the NOx and low sulfur diesel fuels help with SOx. You still have the VOC problem, though. There's also the issue of particulates, which are basically non-existent on an in-tune gasoline engine but are a problem with diesel. On stationary engines, you can put scrubbers on that keep this pretty well under control, but they tend to be big and bulky enough that they're impractical on stationary engines.
As mentioned-especially after the recent VAG and now FCA diesel scandals-I see diesels taking another big step back in the USA on anything other than than large pickups on up to big rigs(and busses).