It's not that one is really better than the other really- just different.
The "14 day learning mode" specifically relates to the 12-24 hour single forecast window. The 14 day learning mode tracks the pressure changes to determine your altitude automatically, necessary for more accurate forecasting.
The "precision forecasting" is the marketing name for our new patented three stage near term forecast we developed in cooperation with an atmospheric science department at UW Madison. It brakes down the country into geographic regions that have specific weather patterns and special conditions that result in our device analyzing the weather data in a specific manner. The result is a breakdown of the next 12 hours of weather in 4 hour increments, including more details like the precipitation chance percentage, and low and high temperature forecasting. The first product with this technology was sold out in canada in short order, with LOTS of positive feedback from consumers on the general accuracy of it.
Of course, we tend to see a higher expectation of accuracy from a device like this from consumers, no free passes like the TV weather man

The end result is around 60-70% accuracy for the 12-24 hour forecast, around the same for the "precision forecasting" on the 01050 so far, although we need more data over a longer timeline to really confirm.
I digress, yes- the 1500 and 1015 will BOTH connect to the 5in1 sensor that comes with the 01050C from costco.com.