Both approaches can work, but they are not identical. Correcting perspective in post is often practical and can produce good results, especially if you have enough resolution and don’t mind extra editing.

A shift lens lets you keep the camera level and move the image circle instead, so you control converging verticals in-camera. That usually gives a cleaner result because you avoid the stretching/cropping that software correction introduces. Post correction can create artifacts and reduces usable frame area, while a shift lens preserves more of the original composition.

That said, shift lenses are not magic: older or cheaper perspective-control lenses can be soft in the corners, and aberrations may increase when heavily shifted, though some of that can be corrected in post.

So the tradeoff is mainly image quality and workflow. If you can capture the perspective correctly in-camera, you’ll usually spend less time editing and retain more image quality. If the shot is only possible with your current lens and software, post correction is still a valid solution. For serious architectural work, a shift lens—or even a view camera—offers more precise perspective control than software alone.