A couple of options spring to mind.

 rsync --dry-run -av --prune-empty-dirs --exclude '*.meta.json' --include '*.json' photos/ photos-copy/

Or if you don't have `rsync` (and why not!?), this will copy the files retaining the structure

 cp -av photos/ photos-copy/
 rm -f photos-copy/*/*.meta.json

This variant will flatten the files into a single directory

 cp -av photos/*/*.json photos-copy/
 rm -f photos-copy/*.meta.json

You can do more fancy things with `bash` and its extended pattern matching, which here tells the shell to match everything that does not contain `.meta` in its name:

 shopt -s extglob
 cp -av photos/*/!(*.meta).json photos-copy/