F2.8 - F5.2
vs.
F3.1 - F5.9
Warning: math ahead
The area of an aperture is defined by the following formula:
pi * (focal_length / f_number / 2)^2
To compare how much more light enters an aperture compared to another aperture, regardless of focal length, the following ratio can be used:
(pi * (2 / f_number_1)^2) / (pi * (2 / f_number_2)^2) - 1
where
f_number_1 is the smaller
f-number (like 2.8, 1.4, etc.).
Using the
f-numbers you provided, the old camera with an
f/2.8 maximum aperture will gather 22.5% more light than the new camera with an
f/3.1 maximum aperture. At the other end of the range, the difference increases to 28.7% more light with the old camera. Like steveash said, better image stabilization in the newer camera may help mitigate the light gathering advantage of the old camera. The higher ISO range on the newer camera will help as well, although it will increase sensor noise.
I should mention that a DSLR camera with a fast prime (fixed focal length) lens is very advantageous in low light situations... This combination at
f/1.4 for example can collect over 100x as much light as a P&S in the same amount of time due to the larger aperture area and higher equivalent focal length. Most P&S cameras have very small sensors so their focal lengths and aperture areas are scaled down significantly compared to a DSLR. This is what hurts their low light performance. Being able to gather more light means you can use lower ISO speeds for better image quality, and higher shutter speeds to reduce camera and subject motion. At lower
f-numbers you also get reduced depth of field which is great visually but tricky to master.