It is impossible for a LHT and DT of the same frame size with the same parts, except for brakesets and hubs (which must be different) to weigh the same, or even within 3 oz. A DT is heavier than a nearly identical LHT build specifically due to differences in the fork, rear dropouts, cable guides, brake cable and housing (longer runs), hubs, and especially the brake calipers. Disc brakes+DT are approximately a 2 lb penalty over a LHT. I've owned both plus a good balance, and I built and weighed the bikes. LHTs with fenders and racks are usually over 30 lbs - DTs the same size are 32+.
You have to be careful when comparing touring bike weights since simply changing a saddle (Brooks) or tires (Schwalbe Marathon) can add 0.3-2 lbs to the bike's weight.
I just weighed my DT for this post - 31.8 lbs, with 1.7 lbs of lights and batteries added from last weighing:
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