Using Perspective Crop is a great feature and if it works for your needs, all the better. However, Lens Correction allows for realtime viewing and a grid for aligning vertical and horizontal lines. IMHO Lens Correction is a more refined tool.

For the purpose of correcting perspective I don’t think there is to much difference between the perspective crop and the lens distortion filter. I do suspect the lens distortion filter might be more precise though. The real difference between the to is that the lens distortion filter has more than just perspective correction, it also has many other options to correct common lens flaws such as chromatic aberration, vignetting, and others.

When it comes to Photoshop there are many ways to do any one thing.