Ubuntu shouldn't be used for web servers to begin with. You should be using a distribution with a long and thorough stable release cycle with minimal packages, such as Debian.
There are two (sometimes more) versions of Ubuntu: Server and Destkop. Desktop is definitely inappropriate for running production web servers (AMI or otherwise), for the reasons you indicate.
Server, however, is perfectly appropriate, especially the LTS release (which is supported for five years). Ubuntu LTS will probably actually be supported longer than (for example) Debian Stable.
The main difference between Ubuntu-LTS and Debian is that Debian's stable release cycle is longer and more thorough. This means that Ubuntu-LTS will have slightly newer software, but Debian will likely have less bugs.
Debian's primary concern with its release cycle is stability. Other distributions like Ubuntu or CentOS trade a little stability for newer software.
My method: Use Debian but when you must have newer versions just add an unofficial repository to your apt sources (assuming you're prepared to deal with the complexity and inconsistency this might introduce).
> The main difference between Ubuntu-LTS and Debian is that Debian's stable release cycle is longer and more thorough.
I believe that the debian stable release cycle is currently at about 2 years, w/ a very short support cycle afterwards. The LTS cycle is 2 years with a 3 years of additional support afterwards.
Ubuntu shouldn't be used for web servers to begin with. You should be using a distribution with a long and thorough stable release cycle with minimal packages, such as Debian.