The ideal solution was really to own both. When the Saturn stopped getting games I grabbed a used PSone, not owning one meant missing out on the likes of Resident Evil 2&3, Metal Gear Solid, Final Fantasy 7, 8, 9 and Tactics, Gran Turismo, Xenogears, Wipeout 2097, Silent Hill, Tekken 3, Castlevania SotN, etc.
I was a Sega fanboy coming from the 16 bit era but imo if you could only own one of them I'd honestly recommend the PSone. If you were a gamer back then you really wouldn't want to miss out on games that literally changed the industry like FF7 or MGS.