Nope. Just one is needed. My recommendation is to stick with the iCloud backup as long as the size does not exceed the limits of iCloud data that you have. With your backup on your computer being 59Gb, you would most likely need to pay for a larger data plan, since only 5GB is included for the free iCloud plan. Some users do backup their photos on a computer in case they get locked out of their account. For more information on the difference between the backup methods, you can check out this support article.
Backup methods for iPhone, iPad, and iPod touch - Apple Support