For example, DuckDuckGo provides both a normal site https://duckduckgo.com and a darknet site https://duckduckgogg42xjoc72x3sjasowoarfbgcmvfimaftt6twagswzczad.onion/ . For me, the onion site is slower but seems to be same in other ways.
Can using Onion sites protect myself as well as the server? Or is it the same for me?
Whether you use Clearnet or Onions, the goal is to protect you and keep you browsing anonymously.
So there is no difference in protection except if the Exit Relay is compromised.
The basic difference is that with Onion you don’t leave the Tor network to go to the Clearnet.
If it is for regular browsing there will be no difference and you will be protected just the same.
If you browse “less common” sites, use the Onion address whenever you can, since you do not leave the Tor network and add 3 more hops to the connection.
Yes. Any time you use Onion sites the data never leaves the Tor network. Traffic correlation is very difficult, and you are protected to a far greater degree from malicious Tor nodes.
Using the .onion duckduckgo site will prevent anyone from knowing anyone even performed a search in the first place, let alone being able to correlate who did it and deduce what they searched for based on what web site was then visited.
Using the .onion can help if traffic from the Tor exit node your current circuit is using is being targeted for traffic correlation.
If an adversary is attempting to correlate your exit server data, seeing a duckduckgo query go out is a cue that a search result is about to be clicked on. It can help correlate the user of the search with the user who clicked on the link.
In short, anything that can deny an adversary information about your search and browsing habits, the time it takes for you to get a search result and click on it, etc, anything that denies them that information is a good thing.