There is one drawback, though, and that is that a stormy-heavy list generally takes big swings. Either they connect and just beat friggin face, or they whiff, and it's a pretty epic failure. There doesn't seem to be any middle ground.
There are more drawbacks, really.
1) They're expensive. You're spending 100+ points on even the smallest useful unit, and full-size units are in the 150-200 point range depending on transport and weapon options. And with only T3/4+ they still die almost as fast as normal guardsmen, so you have to be careful not to spend too many points on your expensive glass cannons.
2) They have to start in reserve to do anything effective. Whether you're outflanking or deep striking you won't arrive until turn 2 at the earliest, and sitting out of the fight until turn 3-4 isn't exactly rare. This can be fine if all you have in reserve is a single suicide melta unit, but if you take multiple large units of storm trooper or flyers and other units that also have to start in reserve you'll find that the ratio of points on the table on turn 1 to points your opponent has on the table on turn 1 starts getting too far in your opponent's favor.
3) They aren't scoring units. While they can obviously do some things better than veterans (for example, deep strike suicide melta) you really have to ask yourself whether they have
enough of an advantage over veterans in the melta/plasma delivery role to offset the fact that they can't claim objectives. Obviously it's fine to take non-scoring units if they give you a substantial increase in power in exchange (I doubt anyone will argue that you shouldn't take Vendettas because they aren't troops), but storm troopers are a lot closer to the "not better enough" line to make them an easy choice.