Sorry forgot to address your second point about how close is Equifax-based credit score to that based on TransUnion. Well, actually they are as close as two credit reports contain the same information - if information is identical credit scores are identical as well. However this is what produces vast differences: (1) hard inquires on one report not on the other (2) the same debt reported differently - a real life example is an investment property mortgage is reported as "Real Estate" in one credit reports while "Other installment" on the other - while primary residence mortgage is "Real Estate" on both reports (3) one report containing correct credit limits information while the other omitting it - have a huge impact on credit utilization calculation (4) when a mortgage is refinanced one credit bureau reports is as a closure of an old mortgage and opening of a brand new mortgage while the other may report is as a continuation of the existing mortgage only with changing lender - and you quickly have a different average account age .....

In some cases these differences don't impact the result as much but in some cases they quickly add up.