Hello there,
A big difference is with the series resistance. The small coated types
usually have much higher series resistance than the frame types.
The frame types usually can handle more current too.
Measure the dc resistance and see what they both measure if you
get another one.
Depending on the circuit, the smaller coil may or may not work. It
depends on several things about what the circuit has to do.
Some boost converters wont start without a low enough resistance,
while others will. Some circuits cant tolerate a bigger resistance
because the losses will be too high.