TLDR: why not both?
Assuming that you are talking about a linear regulator, then one way to look at the situation is to ask these questions;
1) Can a linear regulator do its job when the input is below the require out voltage (plus drop-out voltage)?
2) What does the "un-smoothed" output of a bridge rectifier look like?
These 2 questions lead to #1 being the unavoidable choice, at least for smaller devices. Larger loads may require power factor correction in order to comply with local regulations, which may muddy the waters.
That said, if your design has some kind of particularly 'pulse-like' load, then you would do well to put some local bypassing nearby to that load.
In other words, your #1 option is the usually the best choice, but often there is an element of #2 as well.