During gameplay (I think when you first learn about metamorphosis) you get told about the bonus. I am pretty sure Drippy tells you, and he says you carry over 10% of your stats.
So if your first form familiar has an attack of 100, you will get a 10 point bonus for your second form. This 10 point bonus will then be reduced to a 1 point bonus for your third form. However, you will obvisouly get the 10% bonus from your second form too - but again this might only be 20 points overall.
Overall this really doesn't have much effect, you are unlikely to notice a difference once you have your 3rd forms at a decent level. I tend to level up until I learn all skills, and the do the transformation. It is also best not to evolve them all at the same time, you want to ensure each character has at least one strong familiar to fight with.
You can find more information here, here and here.