Never had Shake Shack, but I tried In-N-Out when I was in California in the summer. It was good but nothing amazing. I ordered the 3x3 Animal Style. The young lady who took my order was extremely nice though and very excited that it was my first trip to an In-N-Out.
My favorite burger in DC was to be found at the Hawk ‘n’ Dove on Capitol Hill, but it’s gone through changes of ownership, remodeling and probably some menu changes since I last ate there.