Motivated by @curl-6’s Xbox threads, it appears that the overall consensus is “more hardware sold =/= more successful.” That said, which would you consider as being the more successful console for Sony?
- PS1 built a brand, established major third-party relations, and did the unthinkable feat of outcompeting Nintendo at their own game... and by a wide margin.
- Meanwhile the latter went on to sell over 160 million hardware units (even with a more competitive landscape now that Microsoft had entered the arena), and simply did everything that the PS1 significantly better. And while more commercially successful, it did give rise to an arrogant Sony during the initial years of PS3, leading to a major fall off in the overall PlayStation brand.

Interesting question.
PS1 established the brand in a huge way. No home console had sold more than NES/Famicom at that point, and PS1 cracked past 100 million units. And DualShock standardized elements from previous controllers and had two sticks.
PS2 was even bigger with GTA games, Sony titles, the added bonus of a DVD player, and so on.
PS2 is more to blame for the arrogance of PS3, but even PS1 shares a little blame as well as it was two generations of Sony dominance.
I'll give it to PS2.

Ps2, I mean it is the most successful console in history. It also demonstrated the ps1 wasn't a fluke and cemented Sony as a gaming powerhouse.

It's a bit of an odd one. When you look at the sales figures one might easily come to the conclusion that the PS2 is more successful. However, would the PS2 have done as well as it did without the PS1? I doubt it. The fact that the PS1 come from nowhere, and still ended up dominating with something like 70% of market share was pretty remarkable.

PS1

I will go with PS1.

1 - the strongest "first console" ever. In a market dominate by Sega and Nintendo, PS1 absolutely humiliated all the competition selling over 3:1 against N64. No console maker ever did such amazing "first console" and manage to penetrate such competitive market.

2 - First console to reach 100m units. It massively expanded the market and blow any possible sale expectations.

If you had been gaming back then (I was), you wouldn't even ask this question. lol. The PS2 was the alpha and omega. It was like a 3D version of the NES. Nothing stood a chance. It swallowed everything and consumed the competition like a black hole. Halo stood no chance. Zelda and Mario stood no chance. Nothing stood a chance. The PS2 is the most dominant 3D dedicated home console to ever grace the market, and by such a large margin that any suggestions to the contrary must be met with suspicion.

More popular: PS2
More sucessful: PS1

PS1 as a newcomer in the market beat down Nintendo, the previous leader, by 3 to 1.

The PS1 had the base controller every single gaming system outside of VR still uses to this day.

The PS1 made optical media the de facto format for games for there on.

The PS1 made Europe a major region for gaming.

It's not even close. The PS2 just sold more.

The PS2 is still the only console that outsold its >100m predecessor, so yeah.