Regarding octaves... they should be universally fine. There are very few designed just for bass, and even those work great on guitar, IME (I once dabbled with an EBS Octabass on guitar).
For volume... doesn't matter.
For overdrive... this is where things can get tricky, since voicing becomes the issue. I wouldn't worry about "too much" low end (because that's usually not going to be an issue, since you're plugging in a guitar, and guitars don't usually pump out that kind of low end). The bigger issue is definitely how the pedal is voiced...
i.e., that dark-sounding mild overdrive you love on guitar might just be too dark and mild for bass, etc., etc.
As far as modulation and time-based effects are concerned, there are rarely "bass-specific" pedals as they tend to be universally friendly. However, there are pedals I've liked better on one instrument than the other, and that's simply due to personal preference.
For the few that do exist...I haven't tried them on guitar.
So realistically speaking, it's extremely difficult to answer your question in regards to most effects... outside of OD/distortion/fuzz, that is (because that's where the question
really applies, IMO!).
If it works great on bass, it'll work great on guitar. But will you like the voicing of the pedal? That's the real question... and I couldn't answer that for you.
On a side note... I
can give you one experience of mine, though it might be a little irrelevant since it regards fuzz. My brother - a guitarist - loves the sound of my MXR Blowtorch on guitar. It seems to be right at home on either instrument. That modern fuzz sound works surprisingly well on the bass' six-stringed cousin.
