In terms of financial efficiency, the Big Y is more preferrable than yDNA-111. Why? Because (let's imagine) that you got the yDNA-111 result for this particular person. You also has the result for another person. There maybe some difference in markers' values or they may be the same. But it doesn't mean anything!!! You can't state for sure when lived the MCRA!!! To get the idea when he lived you need to collect the statistical data for the whole family.
OK, I explain ambiguosly. I will do my best and try to explaim in simpler way. For example, these two persons has 1 mutation. We know that 1 mutation occur 1 time in 150 years (the precise value is not important for the example). Does it mean that the MRCNA lived precisely 150 years ago? No, no and once more - no. It is statistical value got from the populational investigations. The mutations occur sporadically.
But when we look at SNPs and particularly private SNPs from BigY, and better - FGC Y-Elite, test we can be more sure when this SNP was formed. Because every particular SNP mutate VERY rarely and usually is fixed in it's mutated state across generations (of course, back-mutations may occur but they are double rare )))
So to confirm the relationship one should to test all necessary persons with full (or almost full )) Y genome sequencing, compare all SNPs, extract the matching between persons SNPs, try to understand their formation date and make conclusions. After you extract these SNPs specific for your family, clan or branch, you will be able to make extra-test for confirming relationship of another person for belongins to your family/clan/branch. There is option to test somebody for particular SNPs in FTDNA lab and in Y-SEQ lab.