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The Rydberg can be only used for calculating the change in energy between quantum levels for light emitted by H-atoms. DeBroglie's wave equation is used to determine if a particle with momentum has detectable wave properties.
I think it depends on what values you are given and what the question is asking for. The Rydberg equation is usually used when you're trying to find which energy levels an electron is jumping to/from, or when you're trying to find the wavelength of emission when given the energy levels the electron jumps to and from. The De Broglie equation is used when you are given or can derive two of the following three values (since Planck's constant is always given/known) and are asked to solve for the third: wavelength, mass and velocity.
To add on, De Broglie's equation should only be used for particles/objects with mass, never with light. Regarding light and other forms of EM radiation, the main equations to be used will be either v*lambda = c and E = hv.
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