How does fully homomorphic encryption compare to partially homomorphic encryption in terms of security? I found some questions and answers about the performance of Fully and Partially homomorphic encryption. I am interested in a comparison in terms of security guarantees (of any kind, formal or informal). I understand that there are various schemes for both and so a comparison between specific schemes is equally useful to me.

Is, for instance, Paillier/Elgamal more/less secure than FHE (both allow additions and multiplications)?

Is DET/OPE/ORE more/less(probably) secure than FHE (both allow equality and order comparisons)?
In short: They can not be compared, because those cryptosystems are vastly different constructions for different goals.

Taking a step back, usually the security of a cryptosystem is defined with a security parameter $\lambda$, and the security then is described as "... is less than a negligible function $f(\lambda)$ ...", so we can say that e.g. ElGamal with $\lambda = 10$ is less secure than ElGamal with $\lambda = 12$.

But as soon as looking at different constructions, this gets tricky, because they don't compare to the same negligible function any more. Also, they are just upper bounds and there is no statement possible like "it has exactly security $23$".

If you want to combine security with other aspects like runtime, then you run into other issues. Some cryptosystems have fast key generation, others have fast encryption or decryption, etc. There's just one rule of thumb: Quite surely any FHE construction is much, much slower than traditional PKE systems when aiming at similar levels of security. Also, if you consider runtime of a system and include this in your comparison, then you have to keep in mind you are comparing implementations and not the scheme itself.