It's not hard to create a drum map to use Toontrack MIDI files in AD (or vice versa). You'll need to do this as they use different mappings for the kit pieces.
I've done it for my go-to SD kit, and also to use my SD MIDI files in AD. It probably took 20 minutes. I still use the native drum synth when looking for the right loop, but then can drag it into the alternate MIDI map to have it play properly in the other synth (AD midi in SD, or SD midi in AD).
I'm not at my DAW, so this may have the wrong terminology, but the process should help.
Open a Toontrack MIDI clip, with the Toontrack Drum Map.
It mostly involves opening up AD and confirming the Drum Map In for each kit piece (and their various different hits). Then change the Out # in the Drum Map to match the AD IN number notes. You can also change the names if you want, to something that translates better. And drag/drop the rows to put them in a better order.
There's a tutorial somewhere on using Drum Maps. They're not complicated, and can really help with your workflow. I do my programming with a mouse, so I've added rows that have the same instruments at 60% or 120% velocity (for example). It's easier than adjusting the velocity in each note.