Start each engine and see which way the crank pulleys are turning. If they are opposite directions, swapping the starters is not an option.
Voltage drop tests will likely be the easiest way to locate your problem. Using a digital multimeter (DMM), touch one probe to the battery positive terminal (not the wire or connector), then put the other probe on the wire or connector at the same battery post. You should read less than 0.10V across any connection. Anything higher than 0.10V drop and you have too much drop across the connection. Clean the connection, and maybe use some dielectric grease.
Now test the wire itself by touching one probe to the wire or connector you were just at (not the battery post, we already checked that connection), then touch the other probe to the other end of the same wire (or the next connection down that wire). Same deal... if you have more than 0.10V drop, you are losing voltage across the connection. Clean, lube, etc. Continue this test down the line toward the starter, then do the same thing down the ground side back to the battery. You may find a bad connection somewhere. If no problems found, time to look at the starter.
If all of your connections look alright and you decide the starter is the culprit, try cracking it open and cleaning it up first. I just "rebuilt" the starter on my port engine a couple weeks ago with no new parts. Piece of cake (first starter I ever opened up), and it works flawlessly now. It was also easy to flap-wheel the housing and repaint with high-temp Rustoleum while it was apart. Starter looks brand new, works like new, and saved myself some good cash! Red Scotchbrite to clean the brushes and armature, and ultra high temp urea grease on the shaft and bearings was all the parts required for my situation.
Good luck and let us know what you find!