Here I will break down what FTDNA, AncestryDNA, 23andme, FGC, Yseq.net can do and can't do and what kind of testing each company does.

1. Only FTDNA does Y-DNA STR testing and allows matching in it's large database which is the very best way to possibly find a recent common ancestor in the direct paternal line. At least 67 markers are needed to be sure the match is not a coincidence due to convergence. 111 markers are best though. Sometimes, but rarely, two people with a common ancestor in the past 500 years won't match at 37 markers but will match at 67 markers. So if a person is interested in the Y-DNA to possibly prove or disprove a common ancestor in the direct paternal line then the Y-DNA67 is the minimum test a person should get but they can start with a Y-DNA37 and upgrade later. There have already been a lot of people at FTDNA that have proven either common ancestry with their Y-DNA or proven that they are unique and do not match anyone.

2. Only FTDNA, Yseq.net and FGC do advanced Y-DNA SNP testing through SNP packs and/or Next Generation Sequencing. Y-DNA SNPs can rule out a common ancestor and also provide a high likelihood of a common ancestor if two people have an expensive BigY or FGC test. AncestryDNA does extremely limited Y-DNA SNP testing but the results aren't reported and they aren't reliable. 23andme SNP testing is very outdated. They don't even test the most common recent SNPs found in Mexico and Iberia. Two people with the same terminal SNP at 23andme can have a common ancestor from more than 5,000 years ago. So the Y-DNA SNP testing at 23andme is only good enough to possibly determine which SNP pack at FTDNA is needed to find the terminal SNP. Geno 2.0 does more advanced Y-DNA SNP testing than 23andme but it is not as advanced as the Y-DNA SNP testing at FTDNA and FGC and there are a lot of false positives in the test. Even Yseq.net does some SNP testing that Geno 2.0 does not do. If two people have had the exact same test and they have completely different terminal SNPs then that rules out a common ancestor even if there is an STR match at 67 markers. This is one reason why SNP testing is helpful. The other reason is because as Next Generation, SNP pack testing, and testing of ancient DNA remains have become more common certain terminal SNPs have shown to have been in certain regions far longer than thought and there is also a general region that those terminal SNPs originated in. So the terminal SNP is helpful up to a point.

3. Only FTDNA and FGC test the full mitochondrial DNA. FTDNA has the largest database of mtDNA testers and allows matching on the mutations of it's huge database and is cheaper than FGC. 23andme and Geno 2.0 test a lot of the mtDNA but not all of it and they do not do matching. The mtDNA mutates slower than the Y-DNA so it is not as useful to prove common ancestry but there are some cases where it has proven useful at FTDNA. See the ISOGG comparison chart - http://isogg.org/wiki/MtDNA_testing_comparison_chart

4. FTDNA, AncestryDNA, and 23andme do autosomal testing which is the first 22 chromosomes. The autosomal testing is used for possibly finding close relatives and cousins from any of your recent ancestors out to about 5 generations and also for providing an estimate of the ethnic composition that you have inherited from your parents. The further away the common ancestry the less reliable the closeness of the relation of autosomal matches. The common ancestry with a person deemed to be a 4th cousin could actually be from as far back as 8 or even 10 generations ago. This is due to how DNA recombines every generation where some DNA from ancestors is lost and some DNA from other ancestors is maintained for many more generations than average. There is also the problem that we don't have the DNA samples of our ancestors so that we can phase the DNA so the DNA markers are aligned correctly so that the matching isn't mistakenly using alleles from the wrong parent. This does happen. See https://segmentology.org/2015/10/02/anatomy-of-an-ibs-segment/ Each company has it's own database so if you want as many autosomal matches as possible then it is recommended that you get the autosomal DNA test with all three companies.

The overall ancestral origins or “ethnicity” from the autosomal test can vary greatly between companies. 23andme and me has shown to be the most consistent with well documented genealogies and not just for people from Mexico and Iberia but also for most Europeans. AncestryDNA comes in 2nd and FTDNA myOrigins is the least reliably and less consistently matches well documented genealogies. So if the ancestral origins or “ethnicity” is the most important to the tester then the 23andme Ancestry only test is the best one for that.

23andme has the medical or health SNPs included in their more expensive test but being positive for a medical related SNP isn't confirmation that you will have a health problem due to that.

Here is the unbiased ISOGG comparison chart which shows 23andme to have the best biogeographical ancestry analysis (ancestral origins or “ethnicity” calculator) which is also what most people including myself have experienced after comparing hundreds of test results - http://isogg.org/wiki/Autosomal_DNA_testing_comparison_chart

So as a summary, for Y-DNA matching the best option is FTDNA Y-DNA67 or Y-DNA37 then an upgrade if thought necessary, for Y-DNA SNPs get an SNP pack or BigY at FTDNA after the STR test at FTDNA, for mtDNA matching and true mtDNA subclade the best is the mtDNA FullSequence from FTDNA, for autosomal matching use all three companies, for the best ancestral origins or “ethnicity” use 23andme Ancestry only test. Any matching is dependent on who is in the database so if no relatives have tested then you won't have a match. The only way to determine what can be found in your specific case is to get a test. As the databases grow then the chances of finding a match increases so even if you don't have a match now you could in the future.