I think some airlines would prefer a DEC to have previous long haul experience because the DEC will have been there and done that and won't be at the back of a rather mild and fairly short learning curve.
Short haul tend to remain within their own climatological region whereas on long haul it can change from trip to trip, e.g. Singapore this trip east coast of the USA in winter next sort of thing and you may only get to visit some very busy destinations with variable ATC and en route procedures once every two or three months.
When they employ you as a DEC the company is hoping to be buying your relevant experience as well, if they are desperate then they will teach you the differences but would prefer not to have to. My two cents worth.