BTW, most cycling apps I've tried record complete data. They just don't show complete data within the app. Transferring the file to Strava or another app, website or database will often pull out data that was recorded but not readily apparent. However sensors are still needed to record cadence, heart rate, etc.
Cyclemeter is user customizable and shows more data than Wahoo Fitness. The reason I suggest Wahoo Fitness is because it is so simple, very low resource demand so it doesn't drain the battery, but records a lot of data.
I often use both my XOSS G+ computer with sensors and my phone with Wahoo Fitness as a backup. The data usually matches very closely. Even the speed tends to be very similar, despite using a speed/cadence sensor with the computer and relying on GPS for the phone.
The significant differences tend to be calorie estimate (not important to me) and temperature. My XOSS G+ tends to overestimate ambient temperature by about 10 degrees F.