Hand-knotted and hand-woven rugs are both made by hand, however, they each employ a unique weaving technique that affects their quality, texture, design complexity and price. (There are other rugs that claim to be “hand-made,” such as “hand-tufted,” but this is a marketing tactic and not an authentic hand-made technique.)
Hand-knotted rugs are almost always more expensive than hand-woven, as their production process is longer and more complex. They have finer details, are made of better wool (it's length must allow for pile and excess to clip off) and require more skilled artisans.
Weaving a hand-knotted rug requires a great deal of skill and often a lot of time to produce. The quality, and very often cost of a hand-knotted carpet is determined by the number of knots per square inch. In this case a higher density means better quality.
A complex pattern can require very dense knotting and thus it can take a long time to produce. An average weaver can tie about 10,000 knots per day. So you can imagine time it can take to complete one rug, especially if it happens to be a large one. The time involved in making it also accounts for hand-knotted rugs costing more on average.