The most comprehensive testing company is Family Tree DNA. No other testing company offers a significant fraction of the full array of DNA tests for genealogy that you can test at FTDNA. No other company provides functional project support. Genealogists using DNA for their research cluster at FTDNA. At one time, over 90% of all DNA tests for Genealogy were done at FTDNA. Not sure if the number is still that high - but it is quite high. FTDNA has pioneered many of the DNA tests for Genealogy and continues to add new tests at an astonishing rate.
National Geographic continues to limit their yDNA and mtDNA tests to the basic level - but does allow you to transfer your test and sample to FTDNA for free. (you can also transfer your FTDNA results to National Geographic - but don't recall if there is still a fee or if that was waived some years ago) National Geographic's new Geno 2.0 test is potentially very exciting and is considered to be the replacement for FTDNA's old "Deep Clade" test. The Geno 2.0 is sold by National Geographic, but analyzed by FTDNA. If you want success stories on the Geno 2.0, you'll need to wait a bit.
I posted a blog entry about Deep Clade testing a couple of months ago. I was one of the original WTY testers (found a SNP) and am up to date on SNP testing per the Clade projects and ISOGG for my Barton and Hodges families. I have 3 lines trying out Geno 2.0 and I'll update my blog as I receive results http://www.worldfamilies.net/blog/17449
23andMe is focused on only the autosomal block dna test (with a health focus) - but does give haplogroup info for yDNA and mtDNA - as those come from the SNPs they test. You have to pay to transfer from 23andMe to FTDNA
Ancestry has offered a number of different tests through the years, but seems to drop each after a while. The last time I looked, ancestry only offered an autosomal block dna test. ancestry's atDNA test is non-transferrable because they don't provide the underying detail that gives much of the value to researchers.
Disclosure. WorldFamilies (my company) has a business arrangement with FTDNA (since 2004). I have done many of the various DNA tests offered at FTDNA and track more than 30 kits (half of which I paid for or sponsor). I have tested family members at 23andMe, National Geographic and Relative Genetics (who sold out to ancestry)