PSP regularly shared ports with Wii and PS2 on both sides of cross gen transition, it even saw conversions of titles that released on 360/PS3 (e.g Split Second, Midnight Club LA). It was sort of the whole point of the PSP, it was a portable console - that's why I bought it and it far exceeded my expectations.
Sure you had different scenarios; often times a unique title would stand in (Scarface MPR, Godfather Mob Wars, Splinter Cell: Essentials) to a mixed reception, or some content would be cut from the full game (King Kong, 007 From Russia With Love, Star Wars Battlefront 2) but the core gameplay would remain in tact. You also had full ports (Ghostbusters, Star Wars The Force Unleashed, Manhunt 2, Motorstorm Arctic Edge, Gun: Showdown, Justice League Heroes, Marvel Ultimate Alliance, Medal of Honor Heroes 2, Jak and Daxter: Lost Frontier , Spider-Man 3, Burnout Dominator, Fight Night Round 3 etc....) where often times the PSP versions featured bonus content that the home consoles lacked... and then console grade games that were developed firstly for the PSP (Ridge Racer, Daxter, MGS Peacewalker, Miami Vice, Killzone Lib, 2 GTA games, 2 GoW games...etc..) that in some cases were later ported to home consoles because they still had consumer appeal on the big screen. It would be silly for me to list more.
^Despite all of that, I'm not here to defend the PSP as it can handle itself. That thing came out in 2004 and was a monster. It could almost still pass for a cheaper pseudo-contemporary handheld relative to something like the 3DS. It's the single most disgusting piece of dedicated hardware I've seen released in the gaming industry to date, relatively speaking. When I first held it my life flashed before my eyes.
Switch is the latest and greatest as well but the context is different. It was more about getting to a point with power consumption where a dedicated hybrid would become viable and then capitalising on it with the right price point - Nintendo did that. There was a place for that level of hardware and a market for that quality of gaming with the inclusion of added versatility. There's no need to compare the two I think, they're both great and the Switch is the ultimate progression of what PSP initially tapped into.
Also, sorry to inundate the thread with a PSP related tirade.
Wolf 2 looks great.