50 LEDs at 25mA each = 1.25A
If you are using high current capable batteries, then you will get away with it but if not, then neither battery will like having that amount of current drawn from it for long. For general batteries it is best to stay under 1/5 of the amp hour rate, so a 1Ah battery should be run at 200mA or less. 1/10 rate is even better. That said, some batteries are designed for higher loads. Li-ion can take a much higher load, for instance.
That is not to say that you cannot do it, but the batteries might not live very long and will not give their rated capacity.
If you use alkaline batteries, their voltage will drop very quickly under that load, but I guess you are using lead acid (from the 4V) which will cope a little better.