EDIT3: Thanks for very varied answers. I with I could approve two answers and not just one. The question was answered, by both Omegacron and Nate Watson. While Omegacron's answer is much better formatted, Watson's had more relevant examples. My question is about kinetic projectiles like simple shells and debris, not about nukes or chemical weapons, which almost everyone here insists on bringing up. However, these two answers, as well as Jim2B's, paint a complete picture about Federation hulls. Which is "nowhere near as tough as the theory behind them claims"
I've had a discussion with someone, a silly what-if - NCC-1701-x Enterprise vs Battlestar Galactica 2004.
We've been unable to conclude who would get the upper hand - Galactica with it's huge size, incredibly thick armour, rain of metal fire, nukes and armour-piercing explosive rounds that could level Pentagon in a hit, or Enterprise, with it's shields, high-tech, and great, but highly concentrated firepower.
The main problem is that we just can't remember a fight or an example where a Federation ship bigger than a shuttle was hit by a projectile physical. So we can't judge how will Galactica's rain of steel would affect the Enterprise. Our rules were "on-screen events > theory/words" (for example photon torpedoes are said to destroy small planets in Voyager, but in a fight, they struggle to breach shields) and that both ships are moving at a speed they usually are shown to fight at. Slowly.
The only example of physical hit vs shields that I can remember was when the Enterprise-E bumped into a Mogai's wing and lost more than half of it's shield strenght and took minor internal damage, in the movie Nemesis, and I'm pretty sure there were ships destroyed by debris in DS9 and First Contact. I also remember (vaugely) Romulans threatening the Federation with nukes, something the Federation took seriously (on a semi-related note).
I'm looking for an answer compatible with TV shows and movies, not the theory behind them, and I'm looking for both examples where the the damage was mitigated as well as when it was catastrophic.
Also, this is not a Galactica vs Enterprise question, I've only mentioned it because I thought some context would be useful.
EDIT: I am fully aware of Star Trek's inconsistencies, this is why I am asking for examples of both shrugging off the hit AND when it did catastrophic damage. I know there are both. And once again, this is NOT Galactica vs Enterprise.
EDIT2: This is not about nukes! This is specifically about not nukes - kinetic projectiles, be it ammo or debris or meteors or garbage. Not nukes, not chemical weapons, not energy-based weapons. Nukes are different from plain kinetic projectiles. They explode and generate heat, emit radiation, and make a shockwave. a) most of it goes into emptiness, b) space already has a lot of radiation, c) only in atmosphere tl;dr nukes usually are not that dangerous. Now, a small but very very fast projectile can pierce a ship.