In a daytime level, there's no reason to use Sun-Shrooms. They're very expensive during day because you have to wake them up with a Coffee Bean before they'll even produce any sun. Also, you can only build Twin Sunflowers on Sunflowers.
In most of the nighttime levels, start with Sun-Shrooms because they're cheap to start, which is important in the sun-starved nighttime. After a while, Sun-Shrooms will grow up and produce the same Sun as Sunfowers.
In the extra-hard Survival Modes, when you have a very long time to build your garden, you may want to pack Sun-Shrooms, Sunflowers, and Twin Sunflowers. Start with both Sun-Shrooms and Sunflowers, and when your economy is strong enough to support it, upgrade all the Sun-Shrooms to Sunlowers, and then to Twin Sunflowers.