Do you pronounce those differently? Where'd you grow up? In all the English dialects I'm familiar with, those are pronounced the same.
Regardless, it's the "j sound" of "James" (as well as of both "edging" and "aging" for those of you who pronounce them the same) and not the "j sound" of "Jaques" (or the "z" sound of "azure").
(For those familiar with IPA, /be.'dʒiɲ/ not /be.'ʒiɲ/)
If you really want to get pedantic, it should be an unaspirated "ch" (as opposed to q, which is aspirated like "ch" usually is in English). And if you want to get even more pedantic, it's a dual-articulated sound and not a pure postalveolar sound like in English.
That is, IPA [t͡ɕ]
Edit: And if anyone's curious, there are four sounds in Mandarin that English-speakers will interpret as forms of "ch", varying based on aspiration and point(s) of articulation. In Pinyin, all four have distinct romanizations (which is one advantage Pinyin has over Wade-Giles).
Pinyin IPA Articulation Aspirated
ch [ʈ͡ʂʰ] postalveolar retroflex Y
zh [ʈ͡ʂ] postalveolar retroflex N
q [t͡ɕʰ] dual alveolo-palatal Y
j [t͡ɕ] dual alveolo-palatal N
By contrast, English "ch" is postalveolar but not retroflex, and aspiration depends on context: IPA [t͡ʃʰ] or [t͡ʃ].
