Alright, ran the numbers.
So, the homewrecker does 130 damage to buildings at point blank range. It has an attack interval of .8 seconds.
The flamethrower does 6.82 damage per particle at close range, 4.09 at far range (edge or approaching the sentry.). It has an attack interval of .04.
A mini-sentry at full health has 100 HP.
It takes .8 seconds to deal 130 damage with a homewrecker, destroying the sentry immediately.
It takes ~20 particles to deal the same damage with the flamethrower at close range, 14 to do 100 damage.
That means it takes .8 seconds to deal the same damage as the homewrecker, .5 to kill the sentry.
HOWEVER, that is requiring that all particles connect, and the damage is maintained in close range.
So yes, on paper, the flamethrower is more effective in an optimal environment. But in a multiplayer game, there is the requirement of lag compensation, making sure ALL particles hit the sentry, and that you can maintain that distance.
I prefer the burst damage that the homewrecker provides, if you start the swing before you reach the sentry, it does kill it quicker.
There's the numbers, there's my opinion. Do with it what you will.