Depend on the used driver circuit and the exact alkaline design, but it may be worse.
Alkalines have higher open circuit voltage (so the initial LED current may be higher), but they have mostly higher internal resistance then NiCd or NiMh. This higher resistance play an important role in thermal stability of the LED's:
As any semiconductor diode (so include LED) forward voltage decrease with higher temperature, the setup tend to be unstable with the lower impedance voltage source (higher temperature cause lower diode drop, what force more voltage on serial resistance elements, what increase the current, what increase the power dissipation, what increase the temperature further,...).
So here the higher internal resistance make the above explained feedback weaker, so the setup would be less prone to thermal instabilities and runaways.