I don't have hard evidence to back this up, but I would suspect that overfitting is the more prevalent problem. In an overfit classifier, you'll tend to get very good performance on your training data, but see that it does not generalize well to unseen data. An underfit classifier, on the other hand, won't perform very well on the training data, but won't perform much worse on unseen data, either.
In circumstances where the analyst is sloppy in their validation of results, overfit models are very exciting - they appear to be great models, but if you don't properly validate the results, you'll never notice that the model is actually junk. On the other hand, underfit models are not that exciting to begin with - they don't appear to be great models in any circumstance, so they appear less useful at first glance. One can imagine how this can lead to publication bias - overfit models can produce seemingly exciting output, get published, and then never have their performance reproduced on any other data (which is part of the replication crisis in science in general). Underfit models, on the other hand, don't perform that well to begin with, and are ostensibly less likely to be published.
The replication crisis in science strongly suggests to me that most published models are overconfident in their output, and simply do not generalize to independent datasets - this is basically the classic symptom of overfitting. Overfit models will have better performance on some data than underfit models, which plays directly into the well-known publication bias that positive results tend to be published more often than negative ones. Underfit models tend to produce poor but reproducible results, while overfit ones tend to produce good but irreproducible results - the lack of reproducibility in science and the bias toward publishing good results leads me to believe that overfit models get published more frequently than underfit ones.