In fact both of your are saying the same thing. These two methods are named in basic statistics test as critical value method (Where test value is compared with the table value at a particular significance level) and probability value method, commonly known as p-value method in which probability associated with the test value is compared with significance value.
To understand it simply, suppose there are two umpires. One calls a boundary when the ball either hits the rope or crosses it. Another umpire more realistically a robot that compares the area crossed by the ball with the remaining areas (supposing the boundary is at 5% of the extreme area), now the umpire calls a boundary when the remaining area is 5% or less. In short, both of you are saying the same thing.
The most common thing to do is report the Chi-square value, the df (degrees of freedom) and the p-value. Decisions about statistical significance are based on the p-value.