The US happily enforces its own legislation outside of its territory (particularly in the financial world). By almost every single metric, the EU is bigger than the US. You could argue the EU is merely following the US footsteps.
That's far from accurate. The U.K. currently represents around 15% of the EU GDP, which was around 15% higher than that of the US on its own (that includes Norway and Switzerland which are not member but allow me to pencil them in)
If by substantially smaller you mean 'pretty much the same size' then yes you're right.
