I recently played Panzer Dragoon Saga on original Saturn hardware and I have to say that was one of the most profound experiences playing an RPG I've had in my life and playing it on the Saturn itself was a big part of it.
It doesn't help that some of the porting studios sometimes just do shoddy work. Aspyr, for one, can be hit or miss. The Deus Ex remake that's coming out, from what I've seen, is particularly egregious. Just based on the footage I've seen the artistry of the game is completely ruined.
On the flipside - Nightdive doesn't miss. They're the only ones that I will buy their remasters without researching the port quality because they just "get it". The Nightdive remasters of Turok, System Shock, Rise of the Triad, Blood and even some of the more niche ones like Powerslave and Killing time have all been fantastic. Even their full remake of the original System Shock is phenomenal.