I'm a total noob on photography, and I own a Lumix G2 camera. I accidentally broke the default 14-42mm lens, so I'm thinking of getting either a replacement of that or buying a new (more expensive) 20mm pancake lens.
My main focus is to take shots when I go on holiday, either on nice scenery or of people with nice scenery as background.
I would like to learn how to take nice night shots of scenery as well. Which lens would serve these goals better?
The Panasonic Lumix G 20mm F/1.7 ASPH is better. As its name says, it has a maximum aperture of F/1.7 compared to a maximum of F/3.5 at wide-angle for either currently available 14-42mm lenses.
This means the 20mm lets in more than 4X more light and will let you shoot with less light or with the same amount of light at a lower ISO or faster shutter-speed or both.
As a matter you can do even a tiny bit better with the Panasonic Leica DG Summilux 25mm F/1.4.
I have the Panasonic f/1.7 and an Oly kit 14-42mm. The Panasonic is a terrific piece of glass. The oly is OK.
Here's the thing about low-light photography. If you're taking pictures of people, a wide aperture lens is a good thing. When you use a wide aperture, you necessarily get a shallow depth of field. So, you'll get your person's face sharp with some nice bokeh in the background if you focus accurately, and you'll have a short enough exposure to avoid motion blur.
If you're taking landscape pictures without foreground subjects either lens will do the job. The same is true if you're taking landscapes with foreground stuff -- the advantage of the f/1.7 melts away because you will have to stop it down to get the depth of field you want. In that case, spend your money, as somebody else suggested, on a tripod so you can hold your kit steady as you're taking a long exposure.
By the way, you need to learn to use the G2 in aperture-priority mode to control all this well enough to benefit from such a wide lens.
All that being said if you can afford the Pana f/1.7 you'll like it.
Although I love fast, small pancake primes, depending on your use, you may be better served by saving money on the lens and buying a decent tripod. (Around $150; you're wasting your money for less than that, and while it won't hurt to spend more, unless you're very serious about this you don't need to for a small light camera.)
This is because, while the 20mm pancake has a wider maximum aperture¹ and is therefore a faster lens², you may prefer to leave the shutter open for a long exposure³. If you do that, the tripod will reduce blur from camera shake (but not freeze subject motion!), and you'll get an image with more depth of field⁴, which is often desirable⁵ in landscape photographs despite the current fad⁶ for blur.
Many old-school photographers prefer to take portraits with a tripod as well, but I think it's safe to say that these days the majority of photographers prefer the more direct connection of hand-held cameras for this. In any case, unless your subject is very, very still, you'll want to use a faster shutter speed, making the faster lens (in this case, the f/1.7 pancake) the better choice.
References to other questions on this site with good answers that will help you understand all this better:
