What are the key differences between lemons and meyer lemons?

Lemons are quite sour, while Meyer lemons are much sweeter and less acidic. If you substitute directly, it'll have a dramatic effect.

For example, suppose you start out with a dessert made with lemons that has enough sugar added (or little enough lemon juice) to make it the right sweet/sour balance for you. If you replace the lemon with Meyer lemon, it'll be way more toward the sweet side, and won't have the sourness to counteract it anymore. So unless you want that big change, you'd probably want to reduce the sugar and/or increase the Meyer lemon; exactly how you decide to do that would depend on the dessert.

If you substitute in the other direction, Meyer lemon to lemon, you'd likely have to reduce the lemon and/or add a bunch of sugar to keep it from tasting more sour.

Either direction, I don't think it really seems like a good direct substitution. It's a big change, so whether it's a good idea totally depends on whether the original recipe suited your preferences and whether you're okay with a broad range of sweet/sour or have something more specific in mind.

The only things where a direct substitution seems like a good idea to me are things where you're only using the zest. At that point citrus is pretty much all interchangeable, just a different flavor.

When I've used Meyer lemons I haven't noticed Mandarin orange flavors.

Meyer lemons are much sweeter and less sour than normal lemons. I use them in recipes that strongly feature lemon fruit, not just juice.

For example, shaker lemon pies are made with thin slices of whole lemons, including the peel. Regular lemons are overwhelming so I use Meyers.

On the other hand, I wouldn't use Meyers in recipes where lemon juice is used for its acid. For example as a condiment in a lentil soup.

They are harder to juice than regular lemons, at least with reamers or unaided, because the skin breaks apart much more easily (like a plump mandarin orange).