I've never had a Mothra, but I chose to buy the Morino. The bug characters are so cute. With the Morino you have more shell designs to choose from where Mothra only has 2. The Morino also has more characters and the option of changing the temperature when your tama is in its cacoon stage.
I like the Morino because of the screensaver, however, lots of people don't like this feature. The attacks on the Morino are also very cute, because it's either a shoe or a frog tongue.
The Mothra also has the oppurtunity for generation advancement, so that's something to keep in mind.
I don't have a Morino - I have a Mothra - plenty of cute bugs characters to care for as it grows - and the attacks are kind of amusing XD
I would love a Morino - but when it came down to it, I could buy a Mothra much more cheaply than a Morino - there was more choice and a wider range of prices for Mothra tamas than Morinos. However, if price was not an issue, then I would probably have chosen a Morino (for the screen saver feature).