It can, but not always.

From the shared experience here, Perfect Resize may give visibly better enlargements than Photoshop/LR in some cases, especially where edges and shapes are well defined, such as buildings, tree leaves, or strong subject outlines. Compared with standard bicubic-style resizing, specialized enlargement software can sometimes preserve edge detail a bit better.

That said, the improvement is not dramatic in every image, and whether it looks “better” depends on the photo and the final print. For many normal print sizes, modern camera files already have enough resolution that careful resizing in Photoshop or Lightroom is sufficient.

The most practical advice is to judge by test prints, not just by looking on screen. Try the trial version, enlarge the same file in both programs, and compare actual prints at your intended size. If you only print modest sizes, you may not see enough benefit to matter.

A general tip from the answers: if you do resample, scaling by simple round percentages such as 200% can sometimes give cleaner results than arbitrary amounts.