The steering is a little different, but whether it is "twitchy" depends on how wide a bar you go with and how short of a stem.

Shorter stems and narrower bars make the steering faster. Too fast is often called "twitchy".

Think of your hand position relative to the steer tube. In general, the farther forward your hands are, and the farther apart they are, the slower the steering (less twitchy) Conversly, the farther back and the closer together they are, the faster the steering. Try riding with your hands on the hoods, (forward and far apart) and then on the tops with your hands as far in as they go (back and close together) and you'll feel the difference.

So, as far as the difference between drop bars and a flat bar conversion (on the same bike for the same rider):

In general, the grips on a flat bar conversion are a lot farther back (faster) but also a lot wider (slower) than the hood position on a drop bar.

By tweeking the bar width you can make the handling faster or slower.

Also, it should be noted that while sticking a flat bar on the same stem that you had a drop bar on would move the hand position back quite a lot, in reality you often end up running a slighly longer stem with the flat bar. So, your hand position is farther back, but not as far back as it may first seem just by looking at the two different bars.

The bar width aspect (and stem length to some extent) is important in understanding why one poster's attempt here to equate a flat bar conversion with the tops on a drop bar is so absurd.