Hi,
Technically a restore from a backup shouldn't be any different from a simple restart of AEM with a repository in a certain state. The only difference might be, that this state is quite recent (when restarting) compared to restore (it's more distant in the past).
You should analyze the logst to see at which point during startup (or after startup) the difference between a restart and that condition you describe becomes obvious. It might be after the start of a certain service, and then check that service. Or it might get visible in threaddumps.
Anyway, I haven't observed such a behaviour in my experience, so I would assume it is caused by custom code. And in that case any upgrade to a more recent version of AEM will not change that behaviour.
Jörg