RC and RL circuit transient behaviour
which case is dangerous practically for a finite value of source

Nothing is dangerous until you provide real details of the components and the current source that powers the circuits. However, it is likely that the RL series circuit will produce the biggest problem because you are trying to change the inductor current from zero to some non-zero value in an instant and that requires infinite voltage to do so: -
$$V = L\dfrac{di}{dt}$$
That equation is for an inductor and if \$\frac{di}{dt}\$ is infinite (i.e. a sudden change required in current) then the voltage will also be infinite.
It's not initially a problem for the series RC circuit except that the voltage will grow and grow across the capacitor because the current is constant and you are continuously charging it. The voltage will rise to infinity in infinite time theoretically.