Corki's ult doesn't really add much to teamfights, being more helpful for harass and siege. Once you get into a fight you can throw rockets for a little extra damage but it's going to run out of ammo fast if it hasn't already by the time the fight really gets rolling.
Quinn's interesting in that she's one of the most defensive carries. Played her for the first time in a 2v2 the other day against Riven and...hm. I can't remember who the other champ was. Another bruiser type. Anyway, Riven + otherbruiser vs. my Quinn and Ashe. Ashe got gibbed something like 7 times that match; they only managed to catch me twice. Between the knockaway dash/stun/slow for an anti-gap closer, the AE blind to prevent damage if you get collapsed on and the ult to either flee or chase, she's incredibly good for safe positioning. Her lack of consistent steroids (her only major one outside of the melee-range ult is shooting a target clipped by her random-targeting passive, not great for dps) means pretty much any other carry is going to outdamage her in a straight-up fight, but she can get herself out of nasty positions a lot of other carries couldn't and protects herself better than a lot of them. Just pays for it in terms of damage potential which, let's face it, means she's a weaker choice for end-game carrying since she just won't pack the punch of a farmed-up Vayne or Tristana or someone else with a built-in steroid. Draven would hugely outdamage her...but requires a lot of precise movement to do that damage, so I think he'd be a much less safe/consistent pick in the end anyway.
If I were the type to play ranked, I think I'd consider picking Quinn if I saw the enemy team had picked a kill lane for bot. Focus on outfarming them, play super conservative, avoid dying, profit. Don't think I'll be getting her anytime soon, though; I have enough AD carries already.
Corki is in an odd spot. Back in Season 2 he was one of the Holy Trinity of AD carries and now he's rarely if ever seen. Still though I feel his ult adds more to a team fight than Quinn does though his ult is more made for a poke comp. Have a Jayce top, Nidalee mid, Corki bottom and just toss out Corki ults, Jayce and Nidalee Qs. You aren't going to have a team fight really but if the comp works like it is suppose to the enemy should be at a health disadvantage when you do finally engage.
Since I only deal in 5v5s I can't attest to her strength in 1v1 or 2v2s buy you very rarely ever see kill lanes in ranked. Ranked is sickly conventional. Breaking the mold is taboo over there. In normals I'd say I see an unconventional bot one in every five games but in ranked I'd put that up to more of a one in every twenty. I know a few solo laners consider her to have good potential due to her dueling potential as opposed to people who main AD carry say she is lackluster due to her design. Being at 525 range also hurts her. A majority of AD carries are 550+. It feels like she was designed to counter diving bruisers; they gave her safety and took away damage for it.
In the end I feel for 5v5 she is one of those champions who "if I spent X amount of time learning Quinn I could have spent the same amount of time learning Y champion and benefit my team more".
In other news more Rumble nerfs on the PBE. Maybe one day they'll decide he's balanced... (- _ -). Fun fact; other than bug fixes and quality of life tweaks Rumble has only been nerfed since his release in April of 2011. I'm hoping he gets a new skin soon too. In that same amount of time he's had no skin made of him other than the ones he released with. I believe he is the oldest champion to not have a skin made for him since his release skins.