Franklin, a medium sized gas giant in the Beta Virginis system
EuJovians are primarily defined by their mass, which ranges from 0.21 to 8.0 that of Jupiter.
These are the most common among the Jovian Class. Planetary systems with more than one such planet are infrequent, unless the original accretion disk was relatively massive. Typically, with the exception of the local star or other stellar companions, all of the rest of the material of a solar system combined will not mass as much as a single MesoJovian world.
The atmosphere of these planets tends to be very turbulent, flowing in much the same manner as terrestrial oceans, but on a truly heroic scale. Some storms systems can last for hundreds or thousands of years, while others last only a few months. Continent sized thunderstorms are insignificant when viewed from orbit; the night side of the planet is flecked with huge bolts of lightning, tens of thousands of kilometers in length. Everything about a MesoJovian's atmosphere is gigantic.
Mesojovians form near the inner edge of the snow line, and may migrate inwards considerably, or even be flung outwards by interaction with other giants. This means they are found in all temperature classes, and some systems such as 55 Cancri have examples of several different Mesojovian classes.
MesoJovian worlds tend to have many moons, most of which may have been gravitational captured throughout the planet's lifetime. However, they also form true moons, often times massing the same as small planets. Note that any world which has formed near the local star, or has migrated there, is less likely to have moons, since the size of any planet's Hill Sphere decreases with proximity to the star.