Yes. FF sensors are much better for low light work.
Where a crop camera wins is versatility. A 300 mm lens becomes an almost 500mm lens, and you can buy decent ultraw wide angles.
I owned both the 5D II and the 7D (bought the 5D II and 24-105 for $2700). I ran them through their paces in tough light at a dog park across a period of two weeks, which also luckily included some birds in flight. Here's what I found:
1.The 5D II has plain better IQ. Sharper, cleaner, better colors.
2. The 5D II center focus point in AI servo is superior to the 7D center focus point in AI servo in poor light. The difference in noticable.
3. The 5D II's outer focus points are inferior to the 7D's outer focus points.
4. The 7D is built better and feels much better in hand.
5. ISO 1600 on the 5D II looks far superior to ISO 800 on the 7D.
6. There is no comparison in sharpness. 5D II destroys 7D.
7. The 7D's 1.6x crop factor makes it more useful for wildlife, even though 5D II has better IQ.
That said, I kept the 7D, kept the 24-105, and sold the 5D II. I like to shoot wildlife. A lot. I can often be found standing inthe rain with my monpod waiting for animals. The 7D wins for this pursuit thanks to the extra reach and improved sealing. I also shoot landscapes, but the 7D is pretty good at those too at ISO 100. If I shot nothing but landscape/portrait, I would own the 5D II and not the 7D.
I see all these rules applying to the 5D III as well.