Getting stuff from multiple backups

I recently had to get a new iPhone. Luckily I had done a back up a month prior on iTunes, so I used that for my new phone. Everything was good, just missing a month of texts and pictures. While messing around in my settings in my new phone (once the reset was finished) I noticed that I had actually backed my phone up through iCloud right before it broke, must have done it automatically. I redid the setup of my phone with the more recent backup. Come to find not everything was backed up, no pictures at all, all my passwords in safari were gone, and my voicemails. Very strange. I am glad to have important texts back though.

My question is if it possible to pull certain things from backups (like photos or passwords) without having to pull everything. Basically can you pick and choose what you take from as backup. I want to get certain things off of the older backup.

Thanks