I am starting backpacking and there are both internal and external-frame packs. What is the difference, and is one recommended over the other?
I've used both kinds of packs.
External frame packs are generally cheaper, can carry more gear, and allow much better ventilation to your back. In addition to the main compartment and side pockets, most external frame packs also have an area above and below the main compartment where gear can be lashed.
Internal frame packs tend to have larger interior volume, allow more freedom of movement, and (especially in areas prone to thunderstorms) don't have large metallic poles that go above your head. I've seen a few modern internal frame packs that have air channels for ventilation, I've never tried one, but it looks like it may help to keep things cooler.
There really isn't much reason to use an external frame backpack, especially if you're looking at modern backpacks. In almost every case, the internal frame is going to be the better option. Internal frame backpacks have a lot of advantages over external frames, they have a smaller profile, and when properly packed keep weight closer to your center of gravity where you want it. They are more form fitting and give you better maneuverability.
The only advantage I can think of for an external frame backpack is that they are often made up of smaller compartments, where as internal frame backpacks tend to have a primary large storage area and you'll have to rely on stuff sacks for organization.
To add to some of the answers already posted:
External: The biggest advantage is how forgiving an external frame pack is. Since the load is hanging on a frame, you can get away with more casual disregard for how you pack the pack, and don't have to worry about the edge of that pot digging in to your shoulder-blades. It can also take a much heavier load more easily - which is why you will often see trail-crew workers hauling heavy and awkward tools with them.
EFs also tend to be more "idiot-proof" with minimal adjustment options to get wrong (or right for that matter) meaning you can "load-and-go" and ride like a Cadillac down the trail.
Internal: Closer to the body, move more with your body, lower center of gravity, narrower profile. Often better when you anticipate scrambling or hiking off trail. They require a bit more attention when packing, and when fitting, but when properly situated can tend to be more a part of you, rather than something on you.
One possible advantage not yet mentioned for external frame pack is that most are adjustable to fit a wide range of people. This is useful if you know that the pack is going to be used by several people of different sizes, or if the person is likely to be growing rapidly. For example my son who was 14 and 4'11" when the pack was purchased then 16 and 6'1" when he went to Philmont
As a Boy Scout, I prefer the external frame backpack. The internal is more comfortable, but on long hikes, the external is not only practical for more gear, but vents your back so it's not dripping with sweat. I am not as knowledgeable as some on this page, but my strong preference is the external.