Either way is fine although I like yours better. You could have also used the startsWith(String str) method of String. I would suggest you don't worry about efficiency. All things equal, most attempts at making code more efficient tend to fail or is an effort in diminishing returns. I would focus on correctness, documenting your code, and making it easy to read. The person after you who needs to maintain it will be grateful.
Also, notice that this does not detect a string which begins just with the word "not" as the word "nothing" as well as others will pass the test.
Regards,
Jim