restore from different backup

AppleChat wrote:

Just an ordinary common backup of all content.

Migration does not mention anything about different mac models' backups compataibility.

Describe "ordinary common backup of all content."

In regard to the compatibility, the Support Article states:

"Check software, settings, and power

• Install all available Apple software updates on both Mac computers. Install any updates for your third-party apps as well.
• Make sure that your old Mac is using OS X Lion or later. 
• Make sure that your old Mac has a computer name: Choose Apple menu  > System Preferences, then click Sharing and check the Computer Name field.
• Connect both computers to AC power."

The purpose of Migration Assistant according to the Support Article which I previously referenced states:

"Use Migration Assistant to copy all of your documents, apps, user accounts, and settings to a new Mac from another computer.

Migration Assistant copies all of your files to your new Mac so that you don't have to copy your files manually."

It's not possible for me to predict which documents/apps may, or may not be compatible, but AFAIK, there are no system files transferred.

You didn't indicate what kind of backup you possessed, but How to move your content to a new Mac - Apple Support should provide some information to help you define your objectives.