Over at Wallaroo Labs, we've seen some workloads in Docker at are an order of magnitude worse performance for some workloads. However, in those cases, it was comparing raw performance on OSX vs running on Docker on OSX. IO overhead while it exists, has generally been much lower when running in Docker.
Talking about "specifically using Docker" is a little difficult as Docker is mostly providing a UI over existing Linux technologies and thus, isn't that much different from other LXC based technologies.
If you want to talk about "docker specifics", you should be looking at things like the overlay networking and Docker Swarm.
If you want to provide someone an environment where you know your software will work because you've tested that specific environment then containers are a very nice way to accomplish that.
I'm not sure what you consider the "hassle of containerization". I'm not a big fan of Docker. The UX irritates me as I can never remember how to do anything even if I've done it tons before (and in this way, its very similar to git for me), but the creation of containers is, in my mind, quite easy. Certainly no harder than putting together a `bootstrap.sh` with Vagrant.
Without knowing what your run_install.sh does, its hard to really say much beyond that.