Is there any security advantage in searching on duckduckgo using !google? Or is it effectively the same as searching directly on google?
There's no difference: DuckDuckGo doesn't offer any privacy protection when redirecting the search to another result page with a
!google foo (https://duckduckgo.com/?q=!google+foo) just redirects to https://google.com/search?hl=en&q=foo using both
<meta http-equiv='refresh' content='0; url=https://google.com/search?hl=en&q=foo'>
...but not with an actual HTTP redirect, probably in order to hide itself as the referrer:
<meta name='referrer' content='never'>
On the other hand, it prevents Google from getting direct information on the keystrokes and typos through Ajax queries: