I had both, the N64 and the PS1.
Must tell that the marketing compaign got me a little bit for sony ( you know being in your teenage years you don't want to be a kiddy 
), and I reckon that goes for many others as well.
But the biggest problem was the storage on the cartridge: a maximum of 512 MBit! That's just 64 Mbyte(and that just in the last years of that gen)! Even at that time it was incredible low.
PC games started to go cinematic with four disc-games like Under a killing moon and the Wing Commander series three years before the N64 came out, and the PS brought some of this feeling to the console market. The CD-Rom had become the regular standard by that time without a doubt.
Same for the most popular genre at that time: RTS. I loved Command and Conquer, but it needed a long, long time to see it coming to the N64. Not for the PS, it was out quite soon, and developers didn't need to get rid of the cutscenes, voice-overs, even music etc. Remember that's what still amazed people at that time!
Same goes for all the other games that finally came out. Show me one game which wasn't delayed and you'll surprise me. I waited 2 years for harvest moon just to find out, that it wouldn't come out in Europe. Well by that I already had bought the PS-version...
The only things the N64 made better were the controller (in my opinion still the best non-motion controller ever made) and that you could play it with 4 players. And this is actually the reason why I still play some Golden Eye, while I actually never played the PS with friends except for Tekken.
From a nowadays standpoint, the N64 was the system I personally had more fun with, but that's probably due to multiplaying. I keep it in good memory for that, but it's perfectly safe to say, that it's pretty clear why it didn't come in as first.
