Can be compared to: "What is the difference between a PC and a Mac"
GeisorACC is old, it has numeros bugs and security holes. But it's well known, relatively easy to set up, and relatively easy to skin (it got numerous skins to choose from).
ModernACC is newer, and thus more secure. It's very dynamic, but demands more from the user in terms of knowledge and software (PHP 5.3 and so on). Also only SHA1 passwords can be used, and thus you're gonna have problems if you either already have a database with plaintext/MD5 passwords, or do not wish to use SHA1 for some reason.
Long story short;
GeisorACC is old and bugged, but easy to use.
ModernACC is more advanced and secure, but complicated to use.