Is there any method of assigning a numerical score to the extent to which a given alphabet is phonemic? If so, then obviously, the score for a given alphabet would vary across the languages that it was used to transcribe. A great many scores could be assigned to the roman alphabet, since the latter is used to transcribe so many languages. For example, the roman alphabet would score higher in "phonemicness" (phonematicity??) for Serbo-Croation than it would for English.
I don't know of a specific scoring method, but you could probably use a grapheme-to-phoneme conversion approach to make up a reasonable one without too much work.
Say you have a pronunciation dictionary for each of your languages. This maps orthographies to pronunciations:
TEST t eh s t WRING r ih N BEAT b iy t
You could use some kind of alignment algorithm to estimate alignments between the letters and phonemes (Note: below is just one possible, believable alignment):
T:t E:eh S:s T:t W:_ R:r I:ih N:_ G:N B:b E:iy A:_ T:t
Then a really trivial sort of measure might be to just compute the average number of phonemes that are matched to each grapheme and vice versa. The expectation here being that a 'phonemic' system will tend to have more one-to-one mappings, while a mess like English will tend to have quite a few one-to-many / many-to-one mappings.
My guess would be that even this sort of trivial approach would mark a pretty clear difference between say, English and Spanish (I don't know Serbo-Croatian).