Dune: Part Two has been rated PG-13 by the Motion Picture Association, which is the USA's film classification board. This is the same rating the first film received in the states.
As per the MPA's film ratings website, we can see that Dune: Part Two earned its rating for "sequences of strong violence, some suggestive material and brief strong language." This is about what we were expecting, really. In the UK and Europe, we're expecting a similar rating.
Over here, the first part scored a 12, which is often seen as equivalent to the US PG-13. Basically, don't go expecting more extreme violence or anything like that in Dune: Part Two, even if the scales of the battles are likely going to be a bit bigger.