Poor man's filet mignon is a filet mignon that is made from shoulder petite tender meat.
The shoulder petite tender cut of meat is a lean but juicy cut of meat that looks like a small tenderloin and tastes like one as well.
This is why it's known as a poor man's tenderloin or poor mans filet mignon.
In my opinion the Filet Mignon is much better tasting than Ribeye.
However both the Filet Mignon and Ribeye are good meats and are delicious but myself I prefer the Filet Mignon over the Ribeye.
However for some people the Ribeye has more flavor to them and so if they like a really flavorful cut of meat then the Ribeye would likely be perfect for them.
But for those who don't like a really flavorful cut of meat then Filet Mignon would be perfect.
Both are similar meats but the tastes between Filet Mignon and Ribeye are different.
The Ribeye has more flavor to it than Filet Mignon does.