It's depend on what you want to do.
If you except a heavy load, AppEngine is scalable and permit to handle many requests per second. It launch more instances automatically. AppEngine have some free quotas and if you develop your application correctly by using memcache you can stay under these quotas.
Doing service with App Engine is completely different than Apps Script which is juste kind of javascript. You can use Python, Java, PHP or Go on App Engine. And if you want to communicate with other Google's products you need to authenticate which is a little bit more complicated than App Script.