If you just wish to get a straight-line Euclidean distance between two junctions in your street network, then using the Pythagorean theorem for your x/y coordinates is fine. However, keep in mind that the x/y coordinates you are using are based on the dataset's associated coordinate system. Therefore, any "distances" you get from using these coordinates will be based on the units of the coordinate system (which may explain why your values are different than what you are seeing from the measure tool).

In order to obtain useful distance values using this approach without having to do more complex calculations, I would suggest that you make sure that your dataset is in a projected coordinate system (PCS). You can then figure out the distance-measure-of-choice per unit in your PCS, based on your desired distance measure (e.g., you can determine "meters per unit", "miles per unit", etc.).

You can then translate the length of the hypotenuse into the appropriate distance measure using this value. However, you should also make sure that any length attribute you are using in the network dataset for your solves is also based on the same unit of measure, for consistency. Additionally, if your impedance attribute is time-based and not length-based, then you would have to further translate this distance into a valid time estimate instead (e.g., using a maximum expected speed limit).

Does this make sense? Please let us know if you have any further questions.