It is hard to make a definitive statement either way. For example:
> Analysts estimate that underground economic transactions account for one-third (33%!) of the total economy in developing countries and slightly more than 10% of the total economy in developed countries. [0]
On the Bitcoin blockchain it may be around 19% (approximately USD $380bn in yearly transactions on Bitcoin [1], $72bn of which may be illegal [2])
So it's hard to say which "monetary system" is doing better in that regard. Of course, I would argue that cryptocurrencies are still in the experimental phase, trying to figure out where they are going and how.
Once you eliminate the fake transactions, wash trading, tape painting, manipulation, etc, I'd wager you're left with a much much larger proportion of crypto transactions being illicit. Probably close to 100% if you exclude speculation too, since only about 2 or 3 big merchants accept crypto at all.