If you live on the equator side if the tropic, do you get two longest
days of the year, as opposed to one on the polar sides of the tropics.

No, still only one longest day.  However, there are two days when the
sun passes directly overhead, whereas poleward of the tropic, there is
only one day when the sun reaches its highest point (which isn't
directly overhead).

There is a nice plot on Wikipedia, showing a contour plot of day
length versus latitude and day of the year:

http://en.wikipedia.org/wiki/Day_length

It depends on how you define a "day".
(1) If "day" means the time that the center of the solar disk is above
the horizon: If you are exactly on the equator, all days are of equal
length all year long. At all other places, the longest day is the
summer solstice. Note that the June solstice is the summer solstice in
the northern hemisphere, but it is the winter solstice in the southern
hemisphere.
(2) If "day" means the time during which there is daylight -- including twilight:
If you are exactly on the equator, there are two days of maximum
daylight (the two solstices). This is because daylight ends when the
sun reaches a defined angle below the horizon (usually 6, 12, or 18
degrees). The Sun takes just a bit longer to reach these altitudes on
the dates of solstice. If you are not on the equator, the longest day
is the summer solstice.