Are you taking these expressions from two different texts? They may be using different units.
In the second formula you have an additional lambda in the denominator. Maybe one should refer to spectral density in terms of frequency of in terms of wavelength, i.e. ##u_\nu## and ##u_\lambda##.
Why (wavelength) ^4?
Shouldn't it be (wavelength) ^3??
Then dimensions are same
No they are in same page of a book !
Sorry guys, in the first expression this should be ν in the sub script instead of λ.
Ah. Then you are not comparing apples with apples! One is the density per unit wavelength and one is per unit frequency. They would not be expected to have the same units. They are different things.
Separate names with a comma.