For the most part, to the end user, they are equivalent, except under system load.
Apple argue that the reliability of the system increases when using DK as extensions can't crash the kernel anymore.
But the cost of that is the "isochronous" reliability of the extension features (e.g. audio may stutter or drop out).
The kernel extension driver is able to run with elevated privileges, so it is less likely to get interrupted when something else hogs the system. In that regard RME's kernel extension drivers have for me been very stable over the years, especially over Firewire. But USB (2) is more loosely managed.
I think DriverKit client extensions run in the User tier, which means another device has the potential to keep the system more occupied with other transfers (e.g. a Thunderbolt-connected NVMe drive transferring files), instead of filling up audio buffers for uninterrupted playback.
It's clear from RME's video on the subject that RME and Apple have differences in their approach to drivers. I wish they'd collaborate on resolving those differences, so we can again have the "rock-solid" drivers we're used to, even on older interfaces like FF UCX.
Alas, things have been complicated on the M-series Macs. Some people have reported that MacOS Sonoma fixes their issues (i.e. makes Driverkit drivers a viable replacement for Kext). The audio interrupts I experience while doing simple things like previewing a folder of raw photos, have not been resolved in Sonoma. The DK driver reports running out of buffer data to play.
Lastly, that Apple have kept this mechanism around (kext/firewire) suggests that Apple too are more aware of this issue than they'd like to be. Hope this helps.
Fireface UCX, Focusrite OctoPre, Sound Devices MixPre-D, Mac Studio M2 max, macOS Sonoma