In either case, you'll be able to track your progress interactively over the upcoming weeks and months, which is a huge part of what makes these programs intriguing. Both games give you encouragement to keep at it, ask you what's up if you miss workouts, and reward you over time for sticking to the program.

Wii Fit skiing is a blast - you don't even realize the workout you're giving your legs after repeated runs.
The Props
The big advantage of Wii Fit is that it's got a pair of interactive components: the Balance Board and the Remote. This enables the on-screen action to respond to what you're doing. For example, in Wii Fit's jogging game, you're asked to run in place with the Remote in your pocket. As your avatar runs through a cartoony virtual environment, your pace is determined by the movement of the Remote. Jog fast and your on-screen character jogs faster. It's a lot of fun. (Sure, you could fool it by just shaking the controller, but the whole point of the game is to move around, so you're only cheating yourself.) Similarly, the Balance Board also gives you direct feedback, which is especially helpful during the Yoga sessions (more on that below.)
Yourself! Fitness isn't quite as wired. During your workout, your on-screen trainer will stop periodically and ask you how you're doing. Using your controller you can indicate if you're having a hard time or if it was a piece of cake. The game will then use this info to tailor the workout intensity, which is a nice way to organically scale up or scale back your routine. Unfortunately, that's the limit of the interaction.
However, you can use additional props. Yourself! Fitness will tailor a routine around any exercise equipment you might have, including hand-weights, a step, or even a yoga ball. Of course you have to buy these separately. And they're not interactive.
The Presentation
Both games have an animated trainer to help step you through many of the exercises. But beyond that, they're radically different in style.
Wii Fit allows you to use your customized Mii as an avatar, even going to far as to make your Mii fatter or skinnier to represent your body mass index. The whole game is bright, colorful and cartoony. The animated trainers, which are used only for the exercises where you need to see another person to understand the body position, are stylized people (you can choose a male or female trainer). But the game's main spokesman is an awfully cute animated Balance Board. It's amazing how much personality they manage to get from the little animated waffle, who can cheer, wave, or slump over in sadness.
Yourself! Fitness opts for photorealistic graphics (at least as realistic as was possible in 2004 with last-generation tech). The game's spokesperson and your only choice of trainer is "Maya," a realistically-rendered athletic woman with a soothing voice who calmly steps you through a workout and offers advice. You can choose from a number of workout venues (more unlock as you continue to exercise). One of the Yoga locations, a tranquil garden with a nearby waterfall, was particularly well-done.
Wii Fit gets plenty of mileage out of the customized Miis you and your family create. If multiple players are using Wii Fit, you'll sometimes see your family and friends in the background -- running with you in the park, waving at you from the sidelines, etc. While Yourself! Fitness supports multiple profiles, they're never interacting.