The 'mah' reflects capacity, so if a 2600mah battery would run in a light for 26 minutes then a 3100mah one should run in one for 31 minutes before running out. Of course there are other key considerations too, such as whether the claimed capacity is accurate, and that some batteries hold voltage better and so provide the same wattage at a lower current which extends the time between charges above what their relative capacity would suggest.
Also, quality, safety and size are all important considerations which aren't directly reflected by a cell's capacity.