Both literally mean
I make a rule to remember 10 kanji characters everyday.
So what is the difference?
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I am going to say that the difference between the two is fairly subtle. In real life, some people would actually use them interchangeably.
Strictly speaking (at the risk of sounding slightly nitpicky), however, using 「ことにしている」 would often make it sound like the speaker is more serious and more firmly determined about learning 10 kanji a day than when using 「ようにしている」.
It would be like saying "I make it a rule" vs. "I have been trying". 「ように」 could sound slightly less strict about the goal, but again not by much.