I think "tautomer" might be a worse name, even, since the term is usually restricted to explaning why ketones can form enols. Anyway, since nucleons are fermions, just as electrons are, there are strongly analogous properties, such as the presence of discrete energy levels, and the ability to do single-particle excitations from ground-state to excited-state configurations.
However, one key difference in the quantum mechanics involved is that first of all, the discrete-energy-level model (the "shell model") has to take into account the strong interaction, so that so-called spin multiplicity is not preferred for nucleons. Additionally, spin-orbit coupling is very strong in the shell model, so the energy levels become more complicated to deal with. Then you have to throw into the mix the experimentally established existence of nuclear dipole and quadrupole moments, which implies distortion of nuclei away from spherical shapes, which means the shell model becomes less useful in certain regions of the chart of isotopes, further requiring resort to so-called "Nilsson levels" and/or the "collective model", which is used to explain why rotational effects are seen in nuclei.
As far as spectroscopy goes, one major difference is that nuclear rotational/vibrational/single-particle-type excitations all overlap in energy and are often hard to distinguish when sorting out gamma-ray cascades, as opposed to atomic/molecular electron excitaions, molecular vibrations and molecular rotations which all have characteristic energies which are distinct from each other.
Atomic/molecular excitations are usually in the visible-light or X-ray region, while vibrations are in the infrared and rotations in the microwave region.
You can see one of the major reasons why chemical spectroscopy is a lot easier to understand and handle than nuclear spectroscopy.
I could go on for quite some time, but I'll stop here.
Suffice it to say that isomer-states research is important on purely theoretical grounds, since understanding why hold-ups at excited states exist (as far as I know there is no good analog in chemistry for the existence of long-lived excited atomic states; however, phosphorescence does offer a slightly useful analog in understanding how certain "forbidden" transitions lead to a hold-up at a high-energy configuration for some time before leading to a return to the ground state. However, phosphorescence is well-understood and is routinely used as an experimental tool. Nuclear isomerism is still fraught with theoretical models that don't seem to bear out experimentally). As mentioned in the parenthetical statement, grasping more fully why we get isomer states in some nuclei and not others will lead to a better understanding of the basic building-blocks of nature.