Having now had the opportunity to drive the F30 330d back to back over some proper twisty roads alongside my 328i impressions are -
Both are outstanding cars. Having driven the opposition (Audi / Merc) the F30 is a country mile ahead.
The diesel needs a little more coaxing to get its snout to the apex (wet roads), due to the greater weight up front but still very well balanced.
Ability to cover ground broadly the same although you can take the petrol by the scruff of the neck in a way that the diesel does not encourage quite so much.
Diesels performance driven by torque, petrols by revs, because of that you need to be more considered with the throttle in the diesel when exiting corners approaching the limits of grip as it has no lsd.
Brakes much the same, although you are aware the diesel is carrying more weight.
Petrol has a nimbleness about it that the diesel does not have. However, some people may prefer the slightly more "planted" gait of the diesel.
Conclusion is both are first class. Diesel possibly slightly better for motorway journeys, petrol for cross country. You'll choose based on your fuel preference but be delighted with either.