Tried both paths when our daughter arrived. For pure street noise, window work paid off first: interior inserts plus decent curtains knocked down the hiss and random voices immediately. The “thin” ceiling with mineral wool helped room echo and took a bit of sting off the upstairs footsteps, but it didn’t touch the street nearly as much as sealing the glass and frames. If you want a quick sanity check before buying, I spoke with
New York Soundproofing—they explained why the extra air gap from inserts matters for traffic noise, and suggested renter-friendly steps (gaskets, drop seal on the door) that stacked well with the curtains.