Most of these shops use the Mitchell rating system so if you're strictly shopping on price they'll be the same. If you are paying cash then the repair costs will vary. Also, what I've heard is if you tell them at the beginning that it'll be an insurance claim your VIN will be entered in the quoting system and it'll show up on a Carfax search whether you decide to fix it or not in the future.
'15 Ford F150 Lariat SCSB 4x4
'00 740i Sport