Personally, I'd go with the expensive option - you have a grand's-worth of screens there; why not have them both accurately profiled?
The first downside of manual calibration is not knowing which of the two is 'more correct' in the first place - the second is actually getting them both to look the same...
Back in the good old bad old CRT days I always used to set screens up by eye - since I bought a colorimeter, I haven't looked back.
If you do decide to go for a colorimeter, avoid the entry-level Huey Pro, as it no longer works on Mac. Bottom of the line these days is probably the Color Munki Smile, which is quite adequate for 'in-house' calibration, if you don't need a fully-calibrated workflow to printers/publishers etc.
You can also do PCs & your iPhone with it, if you want ;-)
Anyway - if you want to try it manually, the functionality is built right into the OS itself...
System Prefs > Displays > Color > Calibrate... [you get one on each screen, though it doesn't look like you can run both at once]
Clicking that launches the Display Calibration Assistant,
which you can run through as many times as you like; save with a different name each time & review later to see which you're happiest with.
I didn't quite dare to actually run the assistant at first - didn't want to mess up my own calibration ;-) When I did try it I discovered there seem to be far fewer tweakable options than there used to be - you used to be able to adjust per 'gun' colour balance, amongst other things. All I got to pick was a white-point, which really isn't going to be of much use :/