You should visit the embassy with the new/current passport which you will have at the time of stamping and you must carry all your old passports too.
If by the time you go for stamping and you have your new passport handy with you, you should take both passports with you during stamping and finger print scanning at embassy office(s). But, by any case if you don't receive your new passport and your old passport still have atleast 6 months validity after your interview date, then you should carry the Old Passport with you without any issue. Remember, even if you have H1B stamped on your Old passport you can still travel to U.S on your new passport without any issue, just you need to carry both the passports with you.