I think the difference is that we are able to test and understand/verify the operation of the LHC at multiple levels. It's not like they just built what was on paper, flicked the ON switch, and assumed all the data that came out was correct. The components were individually tested and collisions at energies accessible by other supercolliders were done so we could compare to other results.

Unfortunately for medical drugs and psychology, researchers are mostly gathering data without an understanding of the underlying mechanisms. There are also virtually never have proposals which can be tested for compliance with reality in a quantifiable and isolated way as we can with physics, chemistry, or parts of biology.

So I feel the replication crisis is not a matter of various fields just not knowing how to do "good science", but that these fields by their nature make clean hypothesis testing vastly more difficult and p-hacking and statistical trickery (intentional or otherwise) harder to sift out.