Earlier quoted context omitted.
And the SR-71 is so simple the complexity falls off a cliff at the engine, hence your inclination to only care about that in comparing the two. The space shuttle is like a reusable mobile space station, airlocks and all. Occupants of the SR-71 wore space suits the entire time, there's a lot of minimalism on display in the SR-71 which is a large part of what makes it so glorious.
The SR-71 was very complex. For example it had multiple heat exchangers to get rid of heat, to transfer it to the fuel before it was combusted. The titanium structure was complex to maintain. Welding needed to be done in "bubble" work stations under protective gas.
SSME was more or less repeated in results by RD-0120, and rather soon. I'd argue RD-0410 was more complex. SR-71 engine works in two different modes, and even today is not really repeated elsewhere. I think that shows how awesome the SR-71 design was - especially, but not only, for its time.
I'd appreciate a good analysis of design problems and solutions of SR-71 to decide which project was technically more complex.