I've experienced that the MinGW installer is not so great, sometimes. It failed me couple of times with "most recent" or "candidate" ("install an old compiler" strangely always worked).
Bundling compilers with the IDE is also awkward. When migrating from Dev-CPP to code::blocks I found myself in versioning hell. Two bundled compilers, and one manually installed.
There is nothing more annoying than having to guess which compiler and which header file from which version will be used the next time. Yuck.
The strategy that seems to work best for me is:
Download all the .tar.gz files by hand and unpack them into C:\MinGW. Copy all headers in there, too.
No exceptions, no compromises. If anything ever fails, just overwrite that folder. If you want to upgrade to another version or change anything, overwrite that folder.
You know what you get, and you know what you don't get