I'm about to finish my Master in Clinical and Health Psychology and I can tell you that you always have to strive to give the best of your work but remember, as humans, we all make mistakes so I believe it wouldn't be correct to say that you were worst as an undergrad when actually what you had was less experience.
By now, three years after I graduated from University, I can say that I feel more at ease when writing my Masters thesis or when writing a report about a patient of mine but that's because of all the practice that I had as an undergrad and even as a grad student.
You are prepared to write what's demanded of you in grad school, but don't believe me, believe in your self.
Writing in grad school is different that writing for undergrad school only because in undergrad you are sill getting to know your self as a professional, getting familiar with key terms, words and themes, but once you hit grad school, those things will be natural and you'll probably fin it easier to write.
If you have been learning from your mistakes and going the extra mile to get your paperwork the best that you can with the tools that you have and that you've been taught, believe in yourself because if not, that insecurity could be reflected on your writing skills.
Hope this advice is useful and one more thing.
Write about whatever you can at least once a day and keep reading good material because much of what you read is reflected in the way that you write. Remember, practice makes the professional.