We had an E46 325, an E53 3.0, and three other recent BMW six cylinder models. I never noticed that the E53 was louder than any of them. All five were very similar, with the possible exception of the engine note on the Z4 (convertible, and it had a tuned engine sound port into the cabin)

The 3.0 works harder in the E53, so if you are using all of the revs and power that could be it. Something isn't right if it is groaning and resonating, though.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue