I'll trust Visa more not because they've been at it a while, but because the law gives me a good deal of protection against fraud. CurrentC does not use credit cards, it requires direct access to your checking account. That means none of the legal protections against fraud that apply to credit cards. It also means that if their servers get breached, and that bank account information is stolen, the thieves aren't stealing money from the bank, and the bank responsible for getting it back, but rather, they're stealing my money from my bank account, and it's up to me to get it back. And my bank isn't responsible, and the merchant probably isn't either, according to their terms of service, and the people behind CurrentC are likely a shell corporation with nothing to sue them for.
CurrentC looks, to me, like the biggest bucket of bad ideas in the history of electronic payment.