For your question, besides the difference you've mentioned in terms of the construction of sentences, in terms of meaning, there is a slight difference between the two: the former one can be understood as "I am energetic." the later one can be translated into "I tend to be energetic".
"-편이다" emphasizes "a tendency" hereby. So, "rather" is not suitable for the THIS case.
e.g 나는 보수적인 편이다. I tend to be conservative.
This implies that " Yes, I am slightly conservative, but I am not that so(rather) conservative."
Hope this makes sense to you. : )