I myself have eight rares, of which only three are unique (King Krush, Madexx [black], and Gondria). First and foremost, I go for a pet based on looks. If that particular skin has a rare, I will try to get it just because I feel like I specifically "hunted" that beast, rather than tamed Cat # 219,085 out of 1,000,000,000. But, it doesn't always work out to where I like the rare. Case in point, my spider Naphthali. I had every intention of taming Naraxis, but it wasn't up. Went to ZG and grabbed Spider # 934 as a "temp" pet until I could snag Naraxis, to sort of "test-drive" how it looked with me. But then, I ended up falling in love with my over-protective little girl, and even when I stared the rare Naraxis in the face, I just couldn't trade in my "common" pet for the rare version. They are visually identical, no one would have known the difference, but I would have. And the common was more important than the rare because of her personality.
I have also even tamed Loque'nahak and released him...twice. I let him go the first time for something else, then thought I regretted it (I started seeing him all over the place with other hunters and I felt bad), got him restored, then realized I really prefer the less-preferred Gondria (whom I had also let go by this point), and went and got my Shikon back.

I don't care how desired and rare Loque'nahak is, I just don't really care for him.
Then you have my two favorite rares - King Krush and Madexx - who I wouldn't trade for the world. It's not because they're rare (though hunting King Krush was simultaneously thrilling and aggravating), or at least not the only reason. I love them because of their personalities. I was enamored with Apollyon (King Krush) since I first laid eyes on him in the wild. It was more than just, "Ooo, this devilsaur is shiny! Must hab!" It was an immediate bond, before I had even had the chance to tame him. He called to me in a unique way, and I knew I had to have him. With Madexx, I just simply love that scorpion model and wanted one. I got bronze first and liked him alright, but preferred green. I camped and camped and camped for green, but then black showed up. I accidentally tamed him (kinda long story) and tossed him in my stable, not planning to use him. A photo session with friends (who both had Madexxes, and I needed one to take pics with so I just pulled him out) led to yet another very deep bond that I wasn't expecting.
I traded Twinblade from an Outland chimaera to the rare The Evalcharr, realized I really missed my old Twinblade, and dumped the rare for another Outland Chimaera # 48.
So, in my case, I do tend to gravitate toward a rare if it's a skin I already like, but that doesn't mean I'll keep it. The majority of my pets are "common" and I wouldn't have them any other way.
