There are actually four (five if you count the Odyssey version) versions of Cheetah, but you are right in that Priscilla Rich and Barbara Minerva are the two main ones!
I actually prefer the Priscilla Rich version if only because I grew up watching Superfriends, and she was the first version I knew about. She also had a great showing in Alex Ross’s Justice series, which I recommend to anyone and everyone (Giganta is also great in it). However, I’ve loved so many things about Barbara Minerva, particularly in Perez’s run of the book. I just find the name changes very unnecessary.
As for why the Cheetah is her archnemesis:
- She was the one villain that Diana simply could never redeem, even though she constantly tried.
- While Wonder Woman and the Amazons were about celebrating femininity and womanhood, Priscilla despised other women getting more recognition for their accomplishments than she did to the point of insanity.
- She was her archenemy in Superfriends, and nearly all of those match-ups hold true to today (Lex Luthor, Captain Cold, Sinestro, Black Manta).
- Cursed by her god rather than blessed, like Diana.
- While Diana is renowned for her love and compassion, Barbara is reviled for her hatred and greed.
- Diana is very well-spoken and elegant, whereas Cheetah is vicious and savage.
- Cheetah, unlike most characters, is able to handle Wonder Woman physically. I think that’s something we don’t normally see in the major archenemies. Luthor can’t fight Superman without kryptonite-powered armor, Joker can’t fight Batman without using his little tricks, but Cheetah can fight Wonder Woman (and win) in a physical brawl.
One of my favorite aspects of the New 52 version of Cheetah is that they did merge all the versions of her into one.
As for the cons, I’d say the inconsistency in the writing for Cheetah is the biggest one. One issue, you’ll see Cheetah slamming Bane against the wall without breaking a sweat. Another, you’ll see her handcuffed to a lamppost, unable to get away. This is a villain whose strength levels rival Wonder Woman’s (at least, near to it), and she can’t break out of handcuffs on a lamppost? Also, being punched out by Batman isn’t exactly a shining moment for her. I would say the New 52 version has improved, but she was recently defeated by Steve Trevor very easily. So, her biggest con is the fluctuation in her power levels.
I hope that helps! I wish everyone loved the Cheetah as much as I do. :)