It will depend on the apps.
Some simple app settings can be saved on your Google account. For example, on my S4 , under accounts, Google, open my account, there is a 'Sync App Data'. So if I let my new device auto load apps from Google, it will also load the app data.
I have a few apps that I have made sure that I have exported the settings to SD card. I will simply copy those to my Note 4 (if it ever gets here). Then I will need to import those back into the same app on the new device.
I have a number of map apps that have the map file in the SD storage. I will copy those manually.
Verizon also include some form of backup app. I don't use it but it may do what I want.
I run My Backup. It has a few things like my call logs and SMS data that I will import, just for grins.
But for me, for the majority of the apps, I will do a clean install and setup from scratch. Basically, everything will be fresh except my call logs, SMS, offline map files and media.