Was your new bike fit for you? If so, make sure you know your leg extension and fore/aft before swapping the saddle.

To measure your leg extension, place a clipboard on the saddle. Measure from the bottom of the clipboard to the center of the bottom bracket (that's the center of the crankarm -- the lever that attaches your pedals to the bike).

Then, measure from the nose of the saddle to the center of the bar.

You'll want to match these measurements when you put your old saddle on the new bike. This will ensure that your fit is still correct, especially if the two saddles are different (ie one is thicker than the other).