Stryd provides a lot more functionality than Stryd Live.
Stryd Live is mainly intended for use with Zwift on the treadmill, although it can be used outdoors as well, depending on your watch. With Zwift, Stryd Live will provide accurate pace and distance, as well as cadence information.
For Stryd Live users that have a compatible Garmin watch, Stryd developed the Live Companion IQ app. With this app, you get access to additional metrics such as ground contact and vertical oscillation. You will have access to these metrics in Garmin Connect.
The full featured Stryd measures power, and allows you to use power as method to optimize your training and performance. We have detailed Stryd training manual that explains how to train and race with power. In addition to power, Stryd also measures accurate pace, distance and cadence. You will also get access to Form Power, Leg Stiffness, Ground Contact, Elevation, and Ground Contact metrics. Depending on the watch, you will be able to get actual power measurements on your watch (compatible devices and platforms).
If you choose the full featured Stryd, you will have access to PowerCenter to view and analyze your metrics, get information on how to improve your performance, and compatibility with other platforms such as Training Peaks and Strava. The Stryd app for the iPhone and Android can be used to record your run, so you do not need a compatible sports watch.
Stryd Live and Stryd are equally waterproof, have the same battery capacity and same accuracy for pace and distance. It is possible to upgrade Stryd Live to a regular Stryd with a software change. After the upgrade, both devices are nearly identical. The only difference remaining is wired versus wireless charging.