I guess this question on how you define "Successful".

Do you think it can be reasonable argued that the PS4 is Sony's most successful console to date? The obvious other contender is the PS2. It is quite apparent that the PS4 won't be able to match the PS2's hardware total. But is that the only way to compare which of the two even numbered consoles is more successful.

The gaming industry is a lot different than it was in the PS2 era. There was no digital software distribution or paid subscription services both of which are huge parts of Sony's gaming business now. The PS4 has sold more software and made more profit than the PS2. It won't ever reach the mass market ($129) price of the PS2.

Nor was the PS4 ever as dominant against the competition as the PS2 was over its contemporaries.

Sony's 1st party software has also  achieved a new level of acclaim and sale success during the PS4 era.

So what do you say? Is the PS4 Sony's most successful console or is PS2 still the king?

I'm gonna go against the grain and say the PS2. There were about 3,800 games released for it. Nowadays, that's not too much. After all, there are thousands and thousands of digital-only titles. But back then, that was enormous. The PS1 was really the only other console that came close to that physical library in sheer numbers. Now, don't get me wrong. The PS2 had its fair share of shovelware. It undeniably had the most out of sixth generation consoles, but that's to be expected when it was on top.

PS2 was the first console to have a DVD player. While it didn't make much of a difference in it sales, it was an incredible feature for the early 2000s. PS2 also played 95% or more of PS1 titles. And you didn't need an adapter like you did with the Sega Mega Drive (Genesis) to play Master System games.

PS2 had hundreds of titles exclusive to it, from Sony games to a lot of third-party titles. New PS2 hardware also stayed relevant for years and years due to the PS3's early roadblocks. Sony doesn't seem to want to abandon their PS4 base yet (hence some of the new cross-platform announcements) but they've brought PS4 hardware production to a screeching halt, while still technically making the console.

And older consoles don't have DRM bullcrap or microtransactions. That's always nice. PS2 was debatably Sony's last plug and play home console, though PS3 is in some ways (in some ways not).

The PS2 is the best-selling video game platform of all-time, and maybe only the Switch has a chance of beating it.

Back around December 2020, an “analyst” suggested that PS4 is the most profitable console in history (at that time)

So yeah, is Sony’s most successful console.

It's a close call, but I have to give it to the PS2.  A system does have to be profitable in order to be successful (and that is why the PS3 was a failure), but maximizing profit is not the actual purpose of a business.  According to Peter Drucker, the purpose of a business is to make a customer.  Which system made the most customers?  The PS2.

Obviously the PS2 sold the most systems.  However, this is because Sony was actually trying to make the most customers during the PS2 era.  The PS2 was a huge expansion over the PS1.  The PS1 was the best selling system in its day, and yet the PS2 went 50m+ over the PS1's hardware sales.  They kept expanding the PS2 into new markets.  And they eventually dropped the price to $99.99 which was a third of it's starting price.  They were doing everything they could to make new customers.  The PS2 was still profitable during it's $99 price era.  It's not like they were cutting off their own hand to make customers.  Instead they made many new customers while remaining profitable.

On the other hand the PS4 did not make anywhere near this effort to expand into new markets.  Most importantly, it didn't drop the price below $300.  If they were going to do price cuts comparable to the PS2, then they should have at least gone down to $150.  This means that they chose more profits over more customers.  That's a big mark against the PS4.  It is not expensive for them to make PS4's anymore.  They could have easily dropped the price, but they chose not to and that left millions of people out of the gaming market.

On top of that I have to give the PS2 some bonus points for the following reasons:
1. Better software diversity.  A fair amount of those PS4 software sales are people releasing a CoD or Assassin's Creed every year.
2. Bigger game library.  Wikipedia lists PS4 at 3222 and many of those games are digital only.  PS2 has 4380 games and they are all physical.
3. Tougher competition.  The internet is full of people who keep praising the XBox, Gamecube and even the Dreamcast.  In spite of this the PS2 clobbered them all, because it was just that good of a system.  When is the last time you heard someone praising the XBox1?  Somehow it still sold about double what the original XBox sold.  Competition just wasn't very tough during Gen 8.

Basically this. 

While the PS4 is no doubt their most profitable system, even adjusting for inflating, I think the PS2 and even the PS1 were bigger succeses for PlayStation as a brand and Sony as a company, cementing their place as the market leader in an industry they had just entered. They made pretty much the biggest customer base and did it quicker than anyone else had, and as we should all be aware of, brand loyalty is a pretty big deal in the console industry. They set the stage so future consoles simply had to play out their part.

That is a total nonsense statement about the purpose of a business.  Businesses exist to maximize the total return to shareholders (or whatever term you want to use for rhe owners)  That means maximizing profit, generally in the long term.  Getting customers is an important part of that, but a customer is of no value if you do not profit from them.  

Financially PS4
Sales PS2. Just depends on how you look at it.

PS4 uses more standard hardware. PS2 was custom from top to bottom. PS4 also has PSN. PS+. DLC. A lot of paid services. Since Sony looks at $. PS4 to Sony is it's most successful console. For marketing they will say PS2 since consumers look at total sales.

I can't tell you're having trouble with this concept, so let me try to say it again more simply.  The purpose of a business is to serve customers, and the more customers it serves the better.  However, a business that is not making profits is not sustainable in the long term.

On top of that you can measure the Internal Rate of Return (IRR) for any business venture.  Lots of business ventures last more than 1 year, so you have to look at it as a whole.  For example you can look at the PS1 profits over it's total lifetime.  It might have lost money in it's first year, but you can look at the IRR over the console's whole life to see how it has done.  The PS1 was profitable overall.  The PS3 was not.  There are lots of ventures, over a variety of industries, that need to be examined over a time interval greater than 1 year.

That "nonsense statement" comes from the leading business expert of the 20th century.  However, I can understand your confusion.  Some people think a business is there to serve customers.  Others think the business is there to serve themselves.  I am like Mr. Drucker.  I think a healthy business has a purpose in serving customers.  I am not a fan of businesses that make profits such a priority that they do things that are clearly not in their customers' best interest.

I know who he is.

I don't think you understand what a business is.  To all businesses that are bigger than small family firms, and even to most of those, the only thing that matters is return to the owners. Everything a business does it does for the purpose of maximizing that return.  When it gives employees above market wages and a great work environment, it isn't out of the goodness of its heart. A company isn't a human with emotions, it doesn't have a heart. It is done because that is what (they believe) maximizes total return to owners.  The same is true of a company that treats employees poorly.  

In other words, there are no (sizeable) businesses that prioritize profits more than others.  A business, by its nature, does nothing else. 

With all of that said, of course a business needs to create customers.  And it does thay by providing them value.  But, it doesn't provide value for fun, or as an act of charity (even the companies that donate a portion of every sale, or a pair of socks or shoes or whatever aren't doing it as an act of charity in the way that we generally think about that).  A company does this because that's what (it believes) generates the maximum return for owners.

Investing more, cutting investment, hiring, firing, providing good customer service, bad customer service, making cheap crappy widgets, making the highest quality widgets possible, all of it is done for the same reason.