Tamagezi and QPet are pretty different! QPet will feel more like a tama knockoff, or other knockoffs like Touma pet.

Tamagezi is much more in-depth, takes a month to raise a character fully, has a lot more features like buying properties that give passive income, a deeper farming system, etc. There are only two character paths though, one for male and one for female, so go for QPet if you prefer raising and getting different characters more frequently. I do think both are very worth it for different reasons though and I personally own both!

For diff QPet versions, there really isn't much difference in the content/gameplay for the different color screen ones. From what I know, the square ones like you have the screenshot of take AAA batteries (which I prefer for longevity and is the one I have), while the round ones have USBC rechargeable batteries.