I don't see how the question can be answered, without some additional theoretical context. The main problem is that "the same category" sort of suggests a theory of unique categorization of morphemes. If you had asked "is there some conceivable category of linguistic units that includes English prepositions and Japanese postpositions", the answer would be an easy "yes". Instead, it sounds like you have in mind a specific theory of categories, without saying what the defining factor is (for example, various syntactic relation versus certain kinds of functions). Defined in terms of word order, the two sets are clearly different categories (though this consideration is irrelevant for a theory that speaks of "adpositions", a deliberately order-independent term). However, they might be "the same" in some syntactic theory, as a non-head (modifier, complement or some such term). They might be "the same" in one sense, and "different" in another (for example, the syntactic structure might be the same, by some metric, but the semantic function might be different, by some other metric).
A narrower question would be "is the English word just the same category as Japanese X?" (whatever word you want to put in there)". Even narrowing the scope of the English word to pre-NP uses, is "just" a different POS from "with"? That is, how do you justify unifying two morphemes under a single type, in one language? Then, are types the same across all languages?