Related: EC2 Auto Scaling Groups (ASG), Architectures

Vertical Scaling

Increase the size of an instance, resizing.
Each resize causing a reboot – disruption.
Larger instances cost more and may not be in liner way
There is always a cap.

Horizontal Scaling

Increases the amount of instances
Usually requires a load balancer
Sessions is everything, consider it before enabling the concept
Requires an application support or off-host sessions
No disruption
No real limits to scale
Often less expensive, granular