I am not sure how these two sounds are used in Japanese. Which one is more common, in terms of frequency? Under what cases is the other one used?
From The Sounds of Japanese (Vance 2008), p.85:
We'll transcribe [dz] phonemically as /z/ because there's no contrast between [dz] and the voiced lamino-alveolar fricative [z]. Typically, though not consistently, [dz] occurs at the beginning of a word or in the middle of a word immediately following a syllable-final consonant (§5.1, §5.6), and [z] occurs in the middle of a word immediately following a vowel. In short, [dz] and [z] are allophones of this /z/ phoneme. Most native speakers of Japanese are quite surprised to discover there's actually a phonetic difference to worry about, but you'll hear it if you listen carefully to pronunciations of zu [dzɯ] 図 'diagram' and chizu [cɕizɯ] 地図 'map'.
In the above, "a syllable-final consonant" means either
ん /N/ or
っ /Q/, which Vance explains in sections §5.1 and §5.6 respectively. In the latter section (p.108), he goes on to write:
As we saw in §4.3, /z/ has both [z] and [dz] as careful-pronunciation allophones, but following /Q/, /z/ is always [dz].
Although note that voiced geminates like this appear almost exclusively in loanwords, and even there under certain conditions are commonly devoiced—see e.g. A corpus-based study of geminate devoicing in Japanese (Kawahara and Sano 2013) or their other recent work for discussion.