I would have no idea without having the original to work with as there are a LOT of settings that affect this.  There's a lot of noise and sharpening artifacts in your LR and PS examples and some of that "detail" could just be artifacts.

Forge interpolation has a tendency to create smooth edges and works well with a variety of subjects.  If you are going to print sticks and pine needles, sand, tree bark, and other random surfaces where the eye won't catch things like noise and artifacts, something simple like Lanczos might be better.  You could try Lanczos interpolation and see if that works better for those types of images.

Mike

Makes sense.  It's good to experiment.  If you have really specific subject matter like a lot of high frequency detail in nature shots, Lanczos may actually be better than the high-tech methods like Fusion or Forge which try to make cleaner edges on common photographic subjects like vehicles, buildings, people, clothing, macros of flowers, and other things that have solid areas with sharp edges.  Forge will try to make "predictions" about detail and edges which won't be optimal (to the eye) with random sticks, leaves, sand, bark, and those kinds of things.

Think of the above as being similar to your antialiasing (AA) example.  If you take a picture of sand and downsample to 1/4 the resolution, there may be a pixel in the smaller final image that is halfway between a black grain of sand and a tan grain of sand from the original high res version.  In the output, the "correct" thing to do is show that pixel as a dark tan that is halfway between black and tan because it is on neither the black nor the tan pixel.  But that makes a blurry spot in reality and it looks better to the eye if you just pick one or the other (since it's a random pattern).

If you look at the sharpening section under Edit, Preferences, Printing Options, you may also want to try the "static" option.  The smart sharpen option tries to model sharpening after the size (MP) of the original photo vs the size of the print you chose.  All of this stuff is done to try to make your print look the best it can and that's not the same as making print to file result viewed on screen look its best.  So the "static" option sharpens at the finest level of detail regardless of print size and you could play with that.

Mike