Which empire was more successful? Romans or Mongols?

Mongols.

Rome by far....Because Rome built cities, architecture, art, books, libraries, great fortifications, had the worlds biggest cities, had the most riches, lasted (altogether) 1000 years.

The Mongol empire had none of these accomplishments, but were half savages on horseback and in tents, destroyers of cities/ destroyer of civilizations only excelling in trade for awhile and lasting only 250 or so years

the Mongols killed more Humans than all the wars in history put together they were a plague

They have both come and gone, so I would say it is a tie.

If you want to compare them at the peak of their power, I recommend that you compare the following that was under their control:

1. Area

2. Trade

3. Population

I would also suggest you compare how they eventually influenced the civilizations that replaced them.