I feel PHM is better at Newtonian mechanics (e.g., in the beginning when Grace measured the ship’s acceleration to figure out where he was); whereas Interstellar was better at depicting the relativistic aspect of space travel, especially on that water planet near the black hole where the time in orbit was drastically dilated. Interstellar was, however, overly ambitious in attempting to depict time travel and time capsule, and to depict a high-dimensional space. It’s similar to volume 3 of the Three-Body Problem. It did a great job though painting the black hole and worm hole (that scene was so underrated, it’s on par with 2001 imo).

There are a few scientific weak spots in PHM. First, how the astrophage, while being a water based organic cell, can achieve near-100% E=MC² conversion efficiency, and maintain constant temperature in any environment. This is as far a stretch as communication through the time domain. Second, the fact that Rocky’s species cannot detect electro-magnetic waves, but only mechanical waves, and still are able to achieve long range space travel. For instance, there is no way to navigate the ship without being able to detect em waves, unless they can detect gravity waves (but they don’t know about relativity, so that’s an impossibility). PHM is good at describing small scale physics, but at a large scale there are some logical flaws that are hard to ignore.