LED burnt out with 2x AA (or AAA) in series
CR2032 batteries have a lot of internal resistance so the current is limited. It's in the tens of ohms at least. 

A fresh AA cell can supply amperes, enough to easily burn out a small LED. They still have internal resistance, just much, much less.  

The above is the quick TL;DR explanation. To really understand it accurately you'd have to look at the LED voltage vs. current curve and at battery polarization effects which also particularly affect the CR2032. 



According to this graph, the internal resistance starts out at about 10 ohms with 30mA draw and increases in seconds to about 15 ohms (polarization effect). Higher current draw will hasten and increase the polarization effect- the battery can only supply so much current because of the electrochemical reaction taking place. A fresh AA alkaline cell has an internal resistance of perhaps 0.2 or 0.3 ohm.