I don't have hard numbers, but I can say that spam on both sides of the ocean exist. In the US, we get a lot of SMS spam targeted at homeowners, pestering them about selling their property, since there's a lot of open data about property ownership. In Germany, there's frequently spam pretending to be one of the major shipping companies (DHL for example) or the local customs office (Zoll) saying you have a package that couldn't be delivered and to click on a link. I've found the source for this data to be customer data leaks.

So yes, spam is a serious concern. WhatsApp spam exists as well, but since there's a central authority, unlike with SMS, it's a lot harder to avoid being shutdown.