LD150 is absolutely right. We cannot in good conscience recommend any 3rd party recovery service. Due to the Sandbox nature of iOS, extracting data from a backup is nearly impossible. You'd spend a lot of money and likely not get the results you were hoping for. I worked with a guy whose daughter messed up her phone without a backup and they paid over $700 (nonrefundable, btw) to a service who guaranteed they could recover the photos. I advised them to NOT do this. But they spent the money and got nothing in return.
If your backup was corrupted, the chances of you getting anything off the backup are not good to extremely poor. Hopefully you were syncing photos, messages, notes etc. with iCloud. Assuming you were, they are already in the cloud and can be easily moved to your new phone. All the apps you had on the previous phone can be easily downloaded back to your new phone. And this only requires you use the same Apple Account on the new iPhone as you used on the old iPhone.