Restore from backup or start anew?
There different backups at play here:


iTunes backups: saved to local disks, configured in iTunes.
iCloud backups: saved to iCloud, contain more information than iTunes backups, like home screen and app organization.


Both types of backups are often blamed in troubleshooting. But the iCloud backup is especially useful because it has the home screen and app organization. If you have a lot of apps, or you are particular about the way they are laid out on the homescreen, restoring an iCloud backup to a new device is an excellent solution. (Personally, this is what I do when I get a new iOS device.)

Passwords will transfer between devices if you use iCloud Keychain. 

There are numerous downsides to starting from scratch on a new device:


You'll miss out on your old settings that you won't even remember having set, or why, until you're already suffering from not having them.
You'll have to endure downloading your apps manually from the App Store, and chew on the anxiety and worry of wondering if you've forgotten to download one of your most beloved apps, like Flappy Bird.
The time you'll spend configuring your new device from scratch will never pay off, because it is categorically easier for your brain to cognitively consider changes based on your previous settings, than on arbitrary default iOS settings that you should not want to and most likely do not know off the top of your head.


The potential downsides of restoring an iCloud backup seem less:


If you had a lot of apps on your old device, it could take longer than you're willing to wait for them to all install on your new device. But this is only relevant if you would like to downsize the number of apps you use. Otherwise, this is not a downside.
There is a relatively insignificant chance of corruption during the backup/restore process and an additional relatively insignificant change that your previous device was running poorly due to some configuration that may be carried unto the new device via the restore process.


Verdict: If you aren't interested in spending a long time reconfiguring the device from scratch, perform an iCloud backup on your old device and restore unto the new one to save time. After all, time is money.