I know some of the early reviews have said Overwatch struggles on the Switch due to the 30fps cap, muddy textures and the joy-cons, but I've been having nothing but a blast since release, and I've played a fair few hours on the Xbox version since 2017.
To me it feels just like Overwatch should. Perhaps this is because I'm not a hardcore competitive player, and the Switch version is best suited to casuals. The only negative is that character models occasionally take upwards of 10 seconds to load once you begin a game. Hopefully this can be patched out.
Overall, very happy with the Switch version and its great to play in handheld mode.