Many leather bombers come in light, athletic styles. The leather is flexible without needing to be broken in, is lined with a light material, maybe the jacket includes a hood, and the cut and style is more reminiscent of something a baseball player might wear, rather than a pilot. These are great for men with a sporty edge to their look or who live in warmer climates.
Other jackets come lined with a quilted material, giving more warmth to the jacket. The leather may also be of a sturdier, heavier quality.
Even warmer still is the classic, shearling lined leather bomber. This is the perfect jacket for cold weather, as it is very warm and also it can withstand the elements. If you're looking for the classic, rugged look that will keep you comfortable all winter, this is the bomber jacket that you are looking for.
There are several different kinds of leather that are used to make clothing, some of a much higher quality than others. If durability is a concern, top grain or full grain leather, which is cut from the outer hide, will last longer than "genuine leather", which is cut from the inner hide and is generally thinner. "Bonded leather" refers to scraps of leather that are pressed together and chemically bonded, resulting in a low quality material.
While cow hide leather is the most commonly used for jackets, there are many other hide choices out there such as bison, steer, pig or lamb skin, so check those out if you're looking for a different texture and feel.