Hi, Robert. First, the advice you received did not involve a yDNA database larger than FTDNA's; a larger one does not exist. The one you were pointed to is very likely, and very literally, hundreds of times smaller; and I would hazard that upwards of 98% of the data it has came from FTDNA anyway.
For yDNA in particular there is almost nothing to be gained medically in even a full-sequence test like the BigY...there are only about 60 protein coding genes among the Y's 59 million base pairs--compared to, for example, 37 coding genes in the mtDNA molecule's tiny 16,569 bases--and none identified have serious inheritable consequences; the most serious is infertility, not counting rare conditions like XYY syndrome.
The basic FTDNA tests like the 67-marker and 111-marker actually look at what are called Short Tandem Repeats: places where alleles have different numbers of copies...like a copy machine making one extra or one fewer copy.
These tests don't examine protein coding genes at all, and the structure of a coding gene can't be inferred from these repeats. The alleles (like adenine or cytosine) are not directly revealed in the results; only the number of repeats. But they are a great indicator of relatively recent relatedness among men. I took my first Y-STR test in November 2003 and have never hesitated to share those data.