The best pump gas in USA is 93octane? So thats what the USA S4s are mapped for?

In Europe/UK, where gas is reassuringly expensive, our regular gas is 95 octane and premium is 98. S4s are only meant to be run on 98 octane, according to the owners manual and the fuel flap.

So why doesnt the euro S4 make more power than the US S4? I assume you could run much more agressive timing with 98octane before you have knock problems.

as above, the USA uses a different measurement system to Europe

In Europe we use straight RON, the USA uses an average of RON and MON known as AKI, resulting in lower figures.

As mentioned a RON of 97-98 gives a USA (AKI) figure of around 92

Some additional background on this. RON is Research Octane Number and is determined by testing the fuel in a CFR test engine running at 600 RPM  using variable compression an fixed ignition timing.  MON is Motor Octane Number, and is determined by testing the fuel in a CFR test engine at 900 RPM and with heated air/fuel mixture and variable ignition timing.  The average of the RON and MON values, is the AKI, Anti Knock Index rating of the fuel. Waukesha Motor Company, of Waukesha, Wisconsin is the only manufacturer of CFR lab test engines.

See:https://www.asme.org/getmedia/ffedc33f-7e2b-4775-95ec-2f633ddc16f6/50-Cooperative-Fuel-Research-Engine-1928.aspx