I’m primarily a whistler, but some differences I can tell you:
On a flute it seems there is generally more ability to control volume and tone than there is on a whistle, due to the fact that you can change your embouchure on a flute, whereas the soundblade on a whistle is fixed. By changing the shape of one’s mouth when blowing, you can change the tone on a flute by quite a bit, so it does give one more options in that department. You can make the tone nice and hazy, or clear and open sounding, depending on how you blow it.
So, besides the two instruments having a different tone, there are more options for tonal variance with flutes. There are some exceptions, as there are whistles that do offer more in the way of tonal and volume dynamics than other whistles, but a flute allows for more of it. Also, I’ll add that flute is much more challenging to learn at first! It takes a good while to be able to learn to get a consistent sound from it.
And as mentioned, either instrument can achieve the semitones by half holing, but flutes offer the option of adding keys for the half steps away from the hole, which is much easier than half-holing, and also some flutes have keys to play C# and C, so it can play a note that is a whole tone lower than the lowest note on a whistle of the same pitch.
The fingering on both is the exact same on whistle and flute, for both octaves. The only difference in fingering is when there’s keys involved, but the 6 holes are still the same, and not all irish flutes have keys.
Also, flutes usually have better volume for sessions. They are generally more accepted, too. I know some sessions frown upon low whistles (at least as far as I can conclude from a number of low-whistle hating posts I’ve read on some websites. Many sessions don’t mind, though). Soprano whistles and irish flute have been around for a long time, but low whistles have not been a part of the irish musical tradition until more recent history. Many low whistles would have a hard time being heard in a session, too. Low whistle is usually fine, but not everywhere. On the other hand, I don’t think you’ll find many people who object to a flute.
Overall, they are two completely different instruments, though. The low whistle has it’s charms, too, some of which I think the flute can’t replicate exactly, despite the variety they offer.