following the HTTP dialog in curl and browsers like Firefox and Chrome

I honestly wonder, why curl and the browsers do not show you the HTTP status code during your web interactions "by default".

Usually I personally employ curl on the command line with --write-out '… %{http_code} %{url_effective}  …'.

Add-ons for Firefox:

• LiveHTTPheaders
• HTTP Resource Test

Add-ons for Chrome:

• HTTP Headers
• REST console
• Advanced Rest client
• this search will lead you to quite some different tools

Actually in Chrome you can follow the description here, it only employs internal means.