Whenever I drive my car and the engine is at normal operating temp, I can smell oil. Especially when I punch it.

The engine is dry with zero oil leaks and was recently rebuilt from the P's and C's out. It doesn't blow blue smoke or consume excessive oil.

If I leave it idling and sniff around the the oil filler cap I can smell the oil quite strongly still and removing the filler I can see an oily mist swirling around the neck. I have a breather and catch can mounted in the trunk.

Just wondering if this is a characteristic of 3.2 engines as any of the other sixes I've had in the car never smelt this bad and it really detracts from the pleasure of driving my car.

Mine does the same. In fact my whole garage smells of Brad Penn. I think I need a top end rebuild so it could be burning a bit of oil. While it was not yet in the car, between Original Customs and me it was resealed so I doubt there are too many leaks.
I had a 84 911 for a number of years and it didn't smell of oil so I also doubt it is a characteristic... In fact, one of the most popular motors in all 911 history.

I have my "breather" mounted right next to the air intake. That helps getting rid of the oil vapors and smell.