Could you tell us how big the "larger" tank is? If it's still small, 2-3 gallons, a heater might be over heating your betta. Make sure you have a thermometer to check your temp.
There could be a few reasons he is inactive, and the size of the tank might not have anything to do with it. A betta who too hot, too cold, over fed, under fed, living in dirty water, in a high traffic area of the house.. well there are a LOT of reasons he could be acting strange. A little more information would be useful.
It could be that the larger talk needs more hiding places, but some fish simply like smaller homes. Of course, by small I mean 1-2 gallons. Those split 1/2 gallon tanks aren't large enough to sustain even the smallest of lifeforms. Seamonkeys come in larger containers.