To assuage the worries of many fans, Streets of Rage 4 on the Switch is, indeed, totally identical to the PlayStation 4 version. The game's style lends itself beautifully to a handheld experience, and the Switch version also supports four-player local co-op – and yes, two players can use a single Joy-Con so there's no need for extra pads.
The folks over at Eurogamer did a comparison of Streets of Rage 4 on all platforms it's available on, which means PC, PlayStation 4, Xbox One, and Nintendo Switch. There are some key differences between these versions: while PlayStation 4 and Switch versions are identical to each other, but the PC and Xbox versions have different menu options for seemingly no reason. Plus, there seem to be two different PC versions: one from Steam, and the other from the Windows Store, where the latter seems to be the same as the Xbox version.
The menu difference specifically concerns graphics. Some things that can be tweaked on the Switch and PlayStation can't be touched on the Windows Store PC version, while the Steam version has a few extra options. While (the lack of) these options doesn't change the experience all that much, it still seems strange that they were excluded.
All in all, if you're a fan of the genre, this might be a good idea to check out Streets of Rage 4 – and you won't miss out on anything, literally, if you go for Switch instead of PlayStation. After all, why not move with the times?