Melodytchi isn't a cat, but guess she does kind of look like one! I never really thought of that.
I don't know, it really depends on what characters you would prefer to see mixes of... When it comes to the two basic models, Melody and Spacy, it's just the two characters that are different on each, and they also have a special location that has different items in it. The location that needs unlocking is the Mermaid Palace, and by association Gozaru Village. If you don't have another tama, you won't be able to visit the characters from those places. Same thing goes for Dream Mix, who has the same locations, other than the Dream Town (it also has two additional characters too, plus the purple version has Pianitchi iirc)
Now there are two versions of the Anniversary, the normal one and the Gift. I think the Gift goes for cheaper? There's a few differences, mostly a few items, two characters and the gift also has a new location. Now, I have the gift and there's one odd thing about it- to unlock two locations it needs two items that you can't obtain on it, and I have no clue if you can obtain them in any way other than sending them from another tama. If I recal correctly, the normal Anniversary doesn't need another tama to unlock things at all.
Now, I think Sanrio doesn't need a second tama to function. Choose this if you like the characters. I know it can be expensive but I think it's worth it, since it also has one or two gender neutral characters, which is helpful when you want to make your character look a certain way.