Are disk images (.dmg) more secure than executable files (.exe)?

I just bought a Mac computer and noticed that downloads are installed via a disk image while on Windows it was executable files. Are Apple disk images more secure than executable files? Sometimes on a Mac, I'm required to provide an administrative password to permit the continuation of a program install while on windows a vaguely remember having to ever do this? Why is this? Can I open .exe files on a mac (with no boot camp, on Mac OS by default) and vice versa?