Different Effects of Detection Probability Between Presence and Count Data at the Same Location
Disclaimed: Not really an answer, but too long for a comment



If I understand you correctly, this must depend entirely on the accumulated probablity of detection over the entire detection period (the time the cameras were out). If the accumulated probability of detection across all habitat types is high (approaching 1, given that the animal is present), then the detection probability shouldn't be a problem for the binary occurrence variable. An indication of this would be if you have sites (cameras) with either zero or a very high number of occurrences, which should indicate that the binary occurrence is rather robust. On the other hand, if sites have 0-4 occurrences in total it will be extremely difficult to separate non-occurrence from random factors or detectability. I assume that the detection probability across habitats is unknown though (as well as the accumulated probability of detection), but you might be able to make an educated guess. Also, by using a binary response, you will completely exclude the possibility to estimate e.g. an effect of habitat quality (for instance a difference in abundance between habitats), since counts of 1 or 13 will both be represented by 1 in the binary detection variable. In the Q, you talk about "modeling relative suitability" which indicates that you are indeed interested in something similar to this (relative habitat quality). In that case, I think that a binary response will be too coarse to provide useful information.

One possible toy scenario could be that you have two habitat types A and B (10 camera locations/sites of each) with a binary detection variable as:

A: 1 1 1 0 1 0 1 1 0 1  (species found in 7 sites)
B: 0 1 0 0 1 0 1 1 0 0  (species found in 4 sites)

In that case, the species can obviously exist in both habitat types (as you have categorized them), so the higher amount if zeros in B can represent (among other things) 1) lower occupancy of this habitat (in a metapop perspective), 2) that the quality of B is heterogeneous which is not captured by your habitat categorization (so parts of B is just as suitable as A), 3) lower population abundance in B compared to A (but the same detectability), or 4) lower detectability in B compared to A (but the same abundance). I don't really see how you can separate between these cases with only the binary variable, and I don't believe that using a binary detection variable will solve any specific problems compared to using the count data.

This is all very hand-wavy, but can hopefully give you some useful ideas/perspectives.