No, there is no meaningful difference between "even better" and "better still" in this context. If you said either sentence to someone fluent in English, they would understand that you are saying the second suggestion (learning ten new words a day) is better than the first one (learning five new words a day).
As Ram Pillai noted, "even" and "still" are not interchangeable even though they can be used in similar ways. In your example sentences, you had to move the location of "still" to have the second sentence make sense. In other cases, you would have to remove an auxiliary word to be able to use "still", like in the following:
He doesn't like the pay they offered him. Even so, he plans to accept
He doesn't like the pay they offered him. Still, he plans to accept