I would suggest the morino

The umino is very demanding, and quite literally requires your attention all day. The morino is much more lax, and gets attacked by a predator every 3 - 4 hours (I cannot remember which, but attacks occur in a predictable manner on the hour or half hour, making care easier). The characters are adorable, there is no needy baby stage, and the cocoon temperature function is unique. However, the character you obtain on the morino is partially determined by its weight before it enters the cocoon. Sometimes you might wish to maximise its weight as much as possible, which means playing the game a minimum number of times. If you enjoy playing games with your tamagotchis then this version may become a bit boring if you are aiming for a high weight.
Another reason I like the morino is because there are two eggs that you can choose to hatch. One egg potentially gives rise to all the different characters, while the speckled egg gives you Kabutotchi where you try to increase his size, so you can make your decision based on how busy you are etc. There is the screensaver feature which some hate, but I personally like a lot. I like seeing my happy little bug flying around in the trees
The umino isn't bad or anything, but it is demanding, and you will be so happy when it finally goes to sleep each night. But because it is demanding, it gives you a great sense of fulfillment when it eventually survives to adulthood. Unique features like water quality and natural lighting by the sun make the umino another keeper. So I guess it depends on what you're looking for - the umino will need more attention, but both versions are stellar