I think saying something like "in general" is going to depend on what kind of luminescent things you are working with. It might be more helpful to talk about what kinds of things can lead to differences between an excitation spectrum and an absorbance spectrum. I will define them as:

Excitation spectrum: The collection of luminescence at a fixed wavelength while varying the wavelengths of light impinging the sample. This is done at particular angle relative to excitation.

Absorbance spectrum: -log(transmittance). It is a calculated spectrum based on the loss of light making it to the detector after passing through a sample.

Absorbance spectra will be affected by light that is absorbed or scattered. If the sample is turbid, you would expect some kind of background signal that in general has a wavelength dependence on top of your absorbance spectrum. Scattered light just goes somewhere other than the detector. Absorbance spectra are all inclusive.

Excitation spectra, since they rely on a fixed wavelength of detection can be selective of a few things. Most importantly are environmental differences. If your luminescent species is influenced by the polarity/polarizability of its environment (e.g. solvatochromism) and its environment is heterogeneous spacially (e.g. dyes are bound to different parts of a protein that have charges, or different degrees of polarity) or temporally (e.g. polar molecules rotate during the excitation process to differing degrees or the protein reorients), then observing the luminescence at a particular wavelength will select for a subset of the ensemble and distort its spectrum relative to the all-encompassing absorbance spectrum. You can look up something called Red Edge Excitation to get a feeling for this.

If the sample is weakly luminescent, the Raman scatter in the excitation spectrum may be significant enough to distort the spectrum. A measurement of the solvent alone can be used to subtract its contribution.

Fluorescence instruments all have a polarization preference that has to be corrected for when doing polarization/anisotropy measurements. It is possible to preferentially excite one electronic transition over another if there are two transitions with similar energies (e.g. tryptophan).

If the instruments have different bandpasses, then one could blur out the structure seen in another.

I used to work for a fluorescence instrument manufacturer, and in general instruments are not perfect. They are analyzed with standardized tools (e.g. NIST certified black-body radiation sources) and corrected for their idiosyncrasies, but those corrections are not perfect. Depending on the quality of your instrument and how well/recently it was calibrated, you may see some differences between it and a similar one... perhaps from the same manufacturer!

That's all I can think of at the moment. Maybe others can chime in with other things that can differentiate absorbance and excitation spectra. A good resource in general is Lakowicz's Principles of Fluorescence Spectroscopy.