What are the differences between viXra.org and arXiv.org?
From arXiv's website:


  Started in August 1991, arXiv.org (formerly xxx.lanl.gov) is a highly-automated electronic archive and distribution server for research articles. Covered areas include physics, mathematics, computer science, nonlinear sciences, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics. arXiv is maintained and operated by the Cornell University Library with guidance from the arXiv Scientific Advisory Board and the arXiv Member Advisory Board, and with the help of numerous subject moderators.


arXiv has a form of moderation. Users must be "endorsed" by people who have themselves posted papers on the arXiv. (more info) Moreover, a team of moderators is able to reclassify or remove content from the arXiv, for a number of reasons: unrefereeable content, inappropriate format, inappropriate topic... (more info) It also implements some automatic checks for content overlap between papers.

In some fields (e.g. math) it is the standard way of releasing a new paper into the world. At the moment there are 1,369,674 papers on arXiv.

arXiv has a plan to ensure its sustainability and make sure that papers uploaded to arXiv will not disappear from the internet should anything bad happens. There also exists several mirror websites should it even go down.



From viXra's website (in the footer):


  ViXra.org is an e-print archive set up as an alternative to the popular arXiv.org service owned by Cornell University. It has been founded by scientists who find they are unable to submit their articles to arXiv.org because of Cornell University's policy of endorsements and moderation designed to filter out e-prints that they consider inappropriate.
  ViXra is an open repository for new scientific articles. It does not endorse e-prints accepted on its website, neither does it review them against criteria such as correctness or author's credentials.


It was founded by a disgruntled physicist named Philip Gibbs. It is unclear who funds the website today, and it is not even clear who actually runs it today if you just read the website. Compared to arXiv, there is little moderation (according to the FAQ, a paper can e.g. be removed if it's not science/math, if it's plagiarism, if it's obscene and so on, but not if it is obvious nonsense unless it is computer-generated nonsense) and people can submit papers anonymously or under fake names.

At the moment, there are 22,596 papers on viXra.

viXra has no sustainability plans. If whoever runs it decides to take it down tomorrow or their servers catch fire, I'm not sure what would happen.

Warranted or not, it has a reputation of being an alternative to arXiv for cranks and to host a lot of junk science, fake proofs or even outright nonsense. It is not recommended to submit something to viXra if you wish to be taken seriously, because the reputation of viXra would probably taint your paper's reputation by association. (Which is not the same thing as saying that arXiv "bestows credibility" on papers found there. It's rather viXra which bestows a bad reputation.)