When should one use a Tweedie GLM over a Zero-Inflated GLM? I have seen both Tweedie GLMs and Zero-Inflated (ZI) GLMs used in the field of ecology. Tweedie seems to have the benefit of not treating excess zeros separately, as is done using ZI regressions. However, ZI methods seem to be preferred in the literature.
Why would one use Tweedie GLMs instead of ZI GLMs, and vice versa? Are there diagnostic methods post modeling that would cause one to pick one or the other?

Tweedie GLMs are true GLMs and enjoy the usual properties of GLMs.
ZI GLMs are more complex models that assume a GLM plus an extra zero-inflation process, so they are obviously more flexible but at the cost of extra parameters. If the simpler Tweedie GLM fits the data adequately then it is the preferable model. It is doesn't, then you probably need the added complexity of the ZI GLM.
Tweedie GLMs assume that the probability of an exact zero is related to the expected value of the process.
If the expected value is low, then zeros will be more common.
If the expected value is high, then zeros will be less common.
This relationship can be tuned somewhat by choosing the index of the Tweedie model but, if the relationship doesn't hold as expected, then a more complex ZI model may be required.
You can judge the fit of the Tweedie GLM using randomized quantile residuals.
See for example
Interpreting GLM residual plot
or
Poisson regression residuals diagnostic.
You might for example give special attention to the residuals arising from exact zeros in the datasets.
Also see
Can a model for non-negative data with clumping at zeros (Tweedie GLM, zero-inflated GLM, etc.) predict exact zeros?
regarding how to estimate the probability of zeros predicted by a Tweedie GLM.
See also
A model for non-negative data with many zeros: pros and cons of Tweedie GLM
for a related question and answer.
References

*

*Smyth, G. K. (1996). Regression modelling of quantity data with exact zeroes. Proceedings of the Second Australia-Japan Workshop on Stochastic Models in Engineering, Technology and Management. Technology Management Centre, University of Queensland, 572-580.
http://www.statsci.org/smyth/pubs/RegressionWithExactZerosPreprint.pdf

*Dunn PK, Smyth GK (1996). Randomized quantile residuals. J Comput Graph Stat 5(3):236–44. https://www.tandfonline.com/doi/abs/10.1080/10618600.1996.10474708

*Feng, C., Li, L., & Sadeghpour, A. (2020). A comparison of residual diagnosis tools for diagnosing regression models for count data. BMC Medical Research Methodology 20(1), 1-21. https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-020-01055-2
