Always check with the manufacturer about the fuel requirements of your engine. However, both No. 1-D and No. 2-D are intended for use in compression ignition engines. In fact, in cold weather, No. 1-D is blended into No. 2-D or used by itself.
Three of the biggest differences between the two fuels are cetane number, heat content, and viscosity. The cetane number of No. 1-D may be one to two numbers below that of No. 2-D, but still above 40, the required minimum.

Since No. 1-D is less dense then No. 2-D, its heat content, measured in Btu/gallon, will be a few percent lower, leading to a similar reduction in fuel economy.

The lubricity of No. 1-D is likely to be slightly lower than that of No. 2-D because of its lower viscosity. Its lubricity is unlikely to be low enough to cause catastrophic failure. However, a steady diet of No. 1-D in equipment designed for No. 2-D may result in greater long term wear in the fuel delivery system.