`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` while `!$` will result in `$FOO`

This behavior won't necessarily be clear by default but becomes obvious if you use `shopt -s histverify`. With this setting when you use the history expansion feature Bash will not submit the expanded command immediately but display it and wait for you to hit enter again (you may modify it first if required). So we would see something like this after `FOO=bar`:

    $ echo $FOO
    bar
    $ ls !$
    $ ls $FOO  

Then separately...

    $ echo $FOO
    bar
    $ ls $_
    $ ls bar

----

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.