oh lord, you are a newb.
First: Gear Talk. That is where this belongs
Second: They're not even making the Invaders anymore.
Third: Neither one is "better." if one was straight up better, they wouldn't make the worse one.
Here is your answer. The Invaders are thinner and better for urban skiers and skiers who do almost all rails. The Anthems are wider and much better for the whole park, jumps included, even though both skis are practically noodles so you won't be hitting any huge jumps on either of them.
Bottom line: get the Afterbangs.
"I had to hunt down Pretty Ricky and steal back our Doritos."