Detecting grammatical errors from a text is a long-history application. In this paper, we compare the performance of two grammatical error detection techniques, which are implemented as a sub-module of an automated English scoring system. One is to use a full syntactic parser, which has not only grammatical rules but also extra-grammatical rules in order to detect syntactic errors while paring. The other one is to use a finite state machine which can identify an error covering a small range of an input. In order to compare the two approaches, grammatical errors are divided into three parts; the first one is grammatical error that can be handled by both approaches, and the second one is errors that can be handled by only a full parser, and the last one is errors that can be done only in a finite state machine. By doing this, we can figure out the strength and the weakness of each approach. The evaluation results show that a full parsing approach can detect more errors than a finite state machine can, while the accuracy of the former is lower than that of the latter. We can conclude that a full parser is suitable for detecting grammatical errors with a long distance dependency, whereas a finite state machine works well on sentences with multiple grammatical errors.