Mars has much, much less mass than Earth. How would the extra atmospheric mass be kept around the planet without it floating off into outer space? (I mean it doesn't have a strong enough gravitational field.)
The Moon With an Atmosphere
Even before the Voyager encounters with Saturn, astronomers thought that Titan might have an atmosphere. They also thought that there might be oceans of liquid methane on the Moon's surface. When the Voyager spacecraft finally arrived, all that could be seen of Titan was a dense and impenetrable layer of clouds in a thick atmosphere. Titan was found to have an atmosphere more dense than that of Earth and Mars. The atmospheric pressure at the surface is believed to be about 1.6 bars, about 60% greater that on Earth. The atmosphere is composed primarily of Nitrogen with traces of other hydrocarbons such as ethane, hydrogen cyanide, and carbon dioxide. This gives it a rich, orange color. These atmospheric elements are necessary building blocks for life. Astronomers believe that Titan may resemble the Earth at an early stage in its development. They also think that Titan is a prime candidate for the possibility of extraterrestrial life. Titan's surface temperature averages -289°F (-178° C).
http://www.seasky.org/solarsystem/sky3g7.html
Mars is most definately capable of supporting an atmosphere that has the same pressure as Earth.
You have to remember though, that the Atmosphere on Titan has far less kinetic energy than it would on Mars, due to the distance from the Sun... Titan is a kind of frigid analogue of Earth in some senses, with, as you say, an atmosphere abundant in Nitrogen but if this Moon was moved into the Martian orbit, how long would it take this atmosphere to be eroded by the solar wind? Also, does Titan have a strong magnetic field? The Van Allen belts are the only thing protecting our atmosphere from being eroded and blown off into space...
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