Since the Sega Saturn comparisons were pretty one-sided, here's the more interesting comparison that people asked for: the Wii U and the PS Vita.
Both these platforms are very interesting: they both actually had some rather similar ideas (full fledged console gaming, portably), suffered from a lot of the same problems (poor branding, weak third party support), and both led to hardware line contractions for their respective companies.
The PS Vita was a stunning bit of hardware engineering in 2012, with hardware far ahead of its time, and online services that have still not been matched by a portable device. The Vita failed on account of a high cost of entry (Sony mostly declined to drop the price, and you needed a pricey Memory Card to be able to get anything out of the system to begin with), as well as extremely poor support from Sony (Sony refused to acknowledge it at events, dropped first party support for it very early, never marketed it much to the extent that most people are flat out not aware it existed, and many Sony developers publicly disavowed it months after it had come out), and a total lack of third party support, beyond indie games, which the Vita was a treasure trove for. The Vita performed so poorly Sony stopped reporting sales numbers for it to this day, though credible sources place its final tally at 15 million, which is an immense step down from the 80 million+ the PSP sold, and ultimately stopped making handhelds entirely. Nonetheless, the handheld has an incredible library of indie and Japanese games, and remains a high point for Sony's indie game relations.
The Wii U as hardware felt unfocused; it was a system closer to PS3 and Xbox 360 in terms of hardware capability, but it launched just a year before their successors. It was pricey, and that price never really went down through the system's life. That said, it had some very interesting ideas with second screen gaming, remote play, and asymmetric play; while asymmetric play and second screen gaming turned out to be dead ends (Nintendo themselves mostly could not figure out what to do with that functionality), remote play resonated strongly with customers. Wii U's failure was down to very poorly paced and placed first party support (months would go by without a major release from Nintendo; and a lot of games Nintendo put out on the Wii U were the kinds that would never expand the console's mass market appeal), extremely poor third party support, with most third parties publicly disclaiming the system, hampered hardware (the investment in the Gamepad, as well as the hardware being iterative over the Gamecube and Wii's, meant the rest of the hardware was compromised), and, most importantly, catastrophic branding and marketing: Wii U was a terrible name, to the extent that most people who knew of it thought of it as a pricey tablet add on for their existing Wii systems, which they did not want. Most people flat out did not know the Wii U even existed, or what good it was for. Dismal sales of the Wii U ended up poisoning the Wii brand, leading to the console selling only 13.76 million units lifetime, just over 10% of the 100 million+ the original Wii had sold. The failure of the Wii U would lead to Nintendo discontinuing its discrete hardware lines, choosing instead to consolidate handheld and console gaming into one. Nintendo would reinvent itself in the wake of the Wii U's failure, releasing the Switch, which refined the Wii U concept, and is now one of the fastest selling consoles ever. Nonetheless, the Wii U did have its share of successes: its games library was full of beloved games, which are now finding a second life on the Switch; it was the basis which informed Nintendo's approach to third parties and indie developers; and the Wii U had the most full featured suite of online functionality a Nintendo system has ever had, and which the Switch is a regression from.
This is it, then, these are the two big failures PlayStation and Nintendo have had: which is the bigger one, and why?