The violin is typically associated with classical music, which uses the acoustic variation of the instrument. The electric violin is not as widely used, although it is gaining popularity amongst pop and rock musicians. Both acoustic and electric violins have their merits.
Both types of violin are held and played in the same manner. An electric violin is typically a little heavier than an acoustic violin, but this isn't always the case---some electric violins are lighter because their design omits most of the body of the instrument. The difference in size and shape should not pose any real difficulty when switching between the two instruments. A substantial weight difference may feel awkward until a player gets used to it.
An acoustic violin is much cheaper for a beginning violinist. On the low end of the price range, the electric violin itself will usually cost more than the acoustic violin. In addition, an electric violin also needs an amp in order to properly hear the instrument. With mid-range instruments, the prices tend to even out between the two. At the high end, acoustic violins are typically much more expensive since many of them are also irreplaceable.
Electric violins are much better at sound projection than acoustic violins. Electric violinists have complete control of the volume of their violin through the amp. They can also easily position speakers around a room or auditorium. An acoustic violin can be amplified through a microphone, but the results tend to be substandard in comparison to an electric violin. Slight movement in the position of the violinist can alter the volume and tone of the acoustic violin. Electric violins output the signal directly to the amp, removing this issue.
An electric violin is much more flexible. An acoustic violinist has no control over the tone of the instrument beyond what is accomplished through technique. An electric violinist can use all those same techniques, removing any advantage the acoustic violinist might have. In addition, the electric violinist can use the amp equalizer to adjust the tone of her instrument. Like an electric guitar player, an electric violinist can use effects to further modify and control the violin tone.
Tone is subjective depending on the preferences of the violinist and audience. No amount of tone control can make an acoustic violin and electric violin sound identical. In most situations where violins are played, the acoustic violin is more traditional, appropriate and accepted. Less traditional violinists, however, often prefer the more flexible tone of the electric violin.