It probably doesn't give you more security, and in fact if the mixer service's coin volumes are low, which they likely are, and dependent on whatever their turn around time may be, and dependent on how many coins you are asking them to mix, it is very possible for you to get back some of the same coins you sent to them. Unless they were verifiably in a nation which is very unfriendly to whatever country you're in, such as North Korea if you're in the USA, then they likely don't offer any additional security against government agencies compared to a major exchange located in another country, like BTC-e in you're in the USA.
Even if they were to send you different coins, they are still most likely going to be attached to legally questionable transactions due to the very nature of this service. So instead of the block chain showing you received coins from someone who buys Cocaine on Silk Road 2, it'll now show that you received coins from someone who buys Heroin. Either way you still look like a drug dealer.
Sharing Information With Government Agencies / Court Orders
We will NOT comply with any court order for information pertaining to our clients,
nor will we comply with any government request (of any country) for information
about our clients.
But then say:
California Online Privacy Protection Act Compliance
Because we value your privacy we have taken the necessary precautions to be in compliance
with the California Online Privacy Protection Act. We therefore will not distribute
your personal information to outside parties without your consent.
As part of the California Online Privacy Protection Act, all users of our site may
make any changes to their information at anytime by logging into their control panel
and going to the 'Edit Profile' page.
Children's Online Privacy Protection Act Compliance
We are in compliance with the requirements of COPPA (Children's Online Privacy
Protection Act), we do not collect any information from anyone under 13 years of age.
Our website, products and services are all directed to people who are at least 13
years old or older.
So they wont comply with American and foreign court orders, yet they seem to be very concerned with complying with American and Californian privacy laws? Sure sounds odd for a money laundering service.
And although their DNS name is registered to a proxy, and their website is behind the CloudFlare CDN, we can run a reverse DNS query on the IP assigned to their MX entry (18.104.22.168) which tells us that their email server is at a colocation facility in New York because its DNS name is 22.214.171.124.static.nyinternet.net. The banner for that SMTP server identifies its primary domain as mail.bitspeculate.com. We can further prove that both services are ran by the same person because if you create a account at BitSpeculate, login, and go to https://bitspeculate.com/member_area/mtrans_my_accounts and view the HTML for that page you'll see this commented out:
<li class="last"><a href="/contact" title="Contact BitLaunder"tabindex="14">Contact</a></li>
And the twitter account for BitSpeculate says it is ran by Michael Moriarty (which very well may be a pseudonym) in Vancouver BC. The picture for this account is for Professor Moriarty from the recent Sherlock Holmes movie, and according to Wikipedia, Prof. Moriarty is "Sherlock Holmes's archenemy, Moriarty is a criminal mastermind whom Holmes describes as the "Napoleon of crime"." Do you really want to trust you money with someone who fancies themselves as a criminal mastermind? And if you read through the BitSpeculate Twitter account you can't just help but laugh at the irony of someone who runs a exchange and laundering service talking about how online wallets are unsafe.
BitSpeculate itself seems like it very well might be a fraud because after creating a account, I see that they will not tell you the volume of trades for their cryptocurrency markets which seems exceptionally odd for a cryptocoin exchange. And their price data doesn't stream live, but is instead manually inserted in to the HTML via PHP script.
If the sites creator was this sloppy covering their tracks, arrogant in choosing their pseudonym, incompetent in regards to web development, and if I can find out this much about them in a few minutes, I'm pretty sure a government with the ability to subpoena service providers and execute search warrants could find out whatever they wanted to know about this service and its customers with little trouble, regardless of whether or not the sites operators would cooperate or whether or not they are using Tor.
And finally, BitLaunder does not appear to be ran by syadasti. If you read the reddit post you linked, syadasti is running a different service - bitlaundry.com which does not use Tor. If you read the article linked in the reddit post, Mike Gogulski seeming outs himself as syadasti in the comment section by saying he runs bitlaundry.com. And according to Mike's GitHub account he is based in Bratislava, Slovakia. If you google his name some more you can see he was an American who renounced his citizenship, and now has to deal with the trouble of not having a passport and the consequences that brings such as he says "he was once detained by Slovak police outside a bar, beaten and had no one to turn to for consular help." So I'm guessing if a government wanted to force him to reveal who his customers are, it wouldn't be that hard for them to beat it out of him.