Blackmagic all the way, we used them extensively (still do) at the beeb. Their linux driver support is excellent too, the only maintenance I ever needed to do as a sysadmin supporting a fleet of these was occasionally update their firmwares.
A note on Blackmagic hardware in general (including the ATEM switches)- they tend to only work with signals that are fully compliant with broadcast standards. For example, I have some Cisco HD PTZ cameras with a "raw" HDMI output that sends 1080p30 or 1080p60, but there's some wacky difference in the colorspace they output such that my Atomos recorder and Blackmagic capture devices only lock sync when the video level (brightness) of the scene overall is low, such as when you put your hand over the camera. The same cameras work fine with the $25 generic USB capture devices, as well as with the Avermedia BU110 which should be a "true" uncompressed USB3 HDMI capture device (that recently was marked down to $60).
I know Blackmagic is a popular brand for actual cine camera equipment, how do they compare to the more common Elgato 4K60 PCIe? Obviously thunderbolt is nice as an interface rather than the add-in card, but is there anything else it offers above and beyond that?