`man bash`, search for section _Special Parameters_. For `_` you'll find:

> expands to the last argument to the
> previous command, _after expansion_. 

So in a command line context the difference is the expansion. For example if I have a variable `FOO` set to 'bar' and I execute `echo $FOO` then `$_` on the next line will result in `bar` being submitted in the next command while `!$` will result in `$FOO`.

This behavior might not be obvious by default but with `shopt -s histverify` the distinction is a little more evident. (With `histverify` enabled Bash will not submit history expansion immediately after <kbd>Enter</kbd>, it will first display the command, post-expansion, and wait for a second <kbd>Enter</kbd>). So we would see something like this after `FOO=bar`:

    $ echo $FOO
    bar
    $ ls !$ $_
    # We hit Enter and then see
    $ ls $FOO $_ 

`$_` is not expanded until the command is submitted ('parameter expanstion'). It's a subtle distinction but there you go. (Would love to hear of a truly practical use for one vs the other in the comments...beyond the side effects in history and such.)

----

Note that `$_` has different meanings in other contexts:

>  At shell startup, set to the absolute pathname used to invoke the shell or shell script being executed as passed in  the  environment or argument list.

...and...
> Also set to the full pathname used
> to invoke each command executed and placed in the environment exported
> to that command.  

...and...

> When  checking mail, this parameter holds the name
> of the mail file currently being checked.