Okie, first of all it's not a search engine. Tor is a darknet (dark network). It is more about anonymity than privacy.
There are many darknets and the popular ones, in no particular order are:
* Tor
* I2P
* Freenet
There is a new one that is becoming very popular called: Project MeshNet (current implementation is called CJDNS).
There were other attempts but mostly did not take off and disappeared.
All of it relies on sharing your bandwidth with others in the network, so unless you can handle that much, you'll probably find it slow if not very snail.
I2P and Freenet are both closed-darknets. Meaning, they do not provide a gateway back to the regular Internet. Although there are a few users who does provide such but again, these two networks weren't built for that in mind.
So if you want to total anonymity with privacy, I2P and Freenet is the way because there is a far less leak on all fronts (or ends).
Tor on the other hand was built with anonymity as the top priority. Thus it was built to allow "exit nodes". These exit nodes allows the Tor network to access the outside world. This is also the reason why you may find it slow too, if your connect at that moment was thrown into an exit node with a slow connection.
Additionally, Tor is easily plagued with torrent downloads. If people use torrent while their connection is channeled to Tor, the whole network gets affected - resulting to more slowness. However, a few years ago they implemented a new feature for exit nodes to block torrents. But that is not "perfect" especially since torrents can ride almost any ports.
MeshNet I haven't used and I find it very hard to implement, so until then I have no experience to share. But they're poised in taking Tor, I2P, and Freenet by storm.
Now, which is better? That depends on your objective. Tor is very useful if you are aiming for anonymity because you can still access the regular Internet while within the Tor network.
But then again, you can just subscribe to an anonymity/privacy centric VPN like Riseup.net and Autistici.org to name two, or use OpenNIC DNS which adds yet another layer.
Or use I2P (my preferred over FreeNet), which is good for very private communication. It's like joining the darknet of some intelligence agency - you can access the network and communicate with each other, but not use it to access the public Internet.
At the end of the day, anonymity and privacy relies greatly on your settings and practices, especially when it comes to using Tor, VPN, and altDNS like OpenNIC. Always flash your cookies, sessions, don't use your real email, turn-off browser tracking, and so on and so forth. Both mobile and desktop.
If you fail in one, the whole anonymity and privacy effort you did falls into dust. Example. If you use Facebook, and you logged-in to FB via Tor, VPN, or OpenNIC, then you just let FB know another set of IPs that you use. Which will add to your data or profiling. Which makes using Tor, VPN, or an altDNS like OpenNIC useless as far as anonymity and privacy is concerned.
So instead of using FB, you should delete your FB and use Friendica, a decentralized, distributed, privacy-centric social network software. Instead of Twitter, use pump.io, a decentralized, distributed, privacy-centric microblogging software. Then make sure the sites you visit are SSL enabled too, especially if it requires logging-in.
You get the idea
Yes, it is a hassle and requires a change of mindset. Disappearing from the grid - at least in cyberspace - doesn't start with using Tor, I2P, Freenet, MeshNet, VPNs, altDNS, it starts and ends in our minds and practices. Everything else is just a tool, another layer.
And we haven't considered our offline practices like having a social security number, voting every election, your passport, bank records, …
The question now: Is it worth all the hassle?