Both systems are capable of transitions, although they handle them in very different ways. Assuming that the art is already downloaded, then a jump cut in Flash is essentially free. Although it can be very expensive in a digital video to abruptly cut or repeatedly switch between two displays, in a sprite-based system jump cuts are essentially free. Wipes, pushes and slides can be accomplished in Flash, without a significant impact on file size in themselves. Even pure straight cross-fades can be done by animating opacity in Flash, although it's rare to change the alpha of many objects simultaneously.
Timelines are also usually different between types of applications.
Macromedia Flash's timeline is similar to that used in cel animation. Any number of objects can be painted onto one celluloid layer. A single cel layer can also cycle through various pieces of art, as for a walk cycle. Flash's timeline is more similar to a traditional animation system than to a video editor or a 3D animation tool. You can use as many layers as you wish, and put many things on each layer, and motion is applied to a layer rather than to an object on that layer.