It depends on which Euro hitch, there are different manufacturers and ratings. The fact that it is a swan neck design doesn't mean it is necessarily lighter duty; on the E53, the BMW OE swan neck hitch was rated to tow more than the 6000 lbs the NA hitch was rated for.

On the E70, there is a factory option in the UK for "increased towing capacity", separate from the tow bar. Not sure what it includes, but whatever it is may be required in order to achieve a full weight rating for the Euro hitch.

A significant issue for using this design in North America is that the hitch does not include a place to attach safety chains, and so is not legal unless you weld something up.

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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