I can tell you first hand. I was about 12 years old when I decided to buy Sega Saturn over Sony PlayStation, and the coming Nintendo 64 at the time.
What made me choose the Saturn were two things; I used to visit my local arcade once a week (since it was a long drive my parents would take me) and played many great SNK, Sega, Capcom arcade games (Virtual On, Daytona USA, Last Brox, Dead or Alive, Dungeons & Dragons etc.) the one that really enthralled me was Die Hard Arcade (Dynamite Dekka). When I found out it was going to be a Saturn exclusive I wanted the console badly.

It was at 1996 I went to Toys R Us and chose the Saturn bundle which came with three games (Virtua Fighter 2, Daytona USA, and Virtua Cop) shortly after getting Die Hard Arcade for $54.99 at the time. I very much enjoyed my Sega Saturn. From years reading about futuristic CD based systems like CD-i, and 3DO, it felt really awesome to own one. At the time it was very cool to play your audio-CDs as well as games! I would play my favorite soundtracks (at the time) Mighty Morphan Power Rangers: The Movie, The Simpsons Sing the Blues, Weird-Al Yankovic albums, and Now! That's What I Call Music Volume 1.

Mind you besides playing my Saturn I still very much played/rented Super Nintendo games at the time.
For about two years I went to Blockbuster and kept noticing how PlayStation library of games would cover two shelves where the Saturn section stayed roughly the same- small (less than half of one shelf) After renting majority of 'fun' titles that were available I would still have hope for the system. I would read in my magazine subscriptions on games that were being/been released overseas Cyberbots for example, really kept me anticipating a North American release that sadly never came. It became obvious towards the end of 1998 Saturn was going out of the market.

I would visit my friends house and he had a PlayStation which I didn't care for at the time. Since many of the games I loved and rented/owned were also for Saturn (Mega Man X4, Puzzle Fighter, Darkstalkers) BUT it was his older brother which was into more of the obscure titles being released for PS1 that got my attention.
He worked at Toys R' Us and used to buy games, play them for awhile, then return them for a full refund, a trick back in the day. He was into Japanese games, they were; Poy Poy, Silhouette Mirage, and Trap Gunner that got my attention. Also to my surprise he owned a Japanese Sega Saturn (at the time super rare, and expensive to own - you had to order in the back of a video game magazine) and he was running Vampire Savior on it!

The coming Christmas I got Sony PlayStation with Trap Gunner, still own them til this day. My Saturn took a hiatus for a good three-four years until around 2002 I discovered Saturn Torrents and the whole emulation via mod-chips and back-ups. I contributed and played many of the JP exclusive titles for the next years. Same to be said with PlayStation, then Dreamcast.

As for Nintendo 64, I never really cared for the system. It could have been the fact many of my favorite arcade titles were nonexistent on the console. That and I felt, many great games could already pull off the hyped up '360 degree 3-D gameplay' Super Mario 64 bragged about. Jumping Flash, Tomb Raider came to mind. I would play occasionally play Mario Party games over my friends house as well.

I originally posted this over at /r/retrogaming but it makes sense to post it here