It's not unexpected that some new LEAF drivers will be confused by the GOM, or "distance to empty" range estimates.
My understanding is that the Tesla S has the concept of "rated range", which directly correlates to remaining charge and not to one's driving history. A Tesla S with a brand new, fully charged, room temperature 85 kWh battery should have a rated range value of 265 miles, corresponding with the EPA's range rating on the car. The Tesla S can also display a "predicted range" value which depends on driving behavior/conditions.
By contrast, the LEAF only displays a predicted range value which while better in the 2013 model is prone to fluctuation. There is no "rated range". Look at the SOC value or charge bars for a better idea of how much charge you have left.
2011 LEAF at 71K miles, pre-owned 2012 Tesla S 85 at 98K miles
LEAF battery: 9/12 bars and < 49 Ah (-28% vs. new)
Tesla battery: 250+ miles of range (-5% vs. new)