I keep seeing many, many posts on FB asking which tax preparer will get them the biggest refund. This doesn't even make sense to me. Your 2014 numbers are already done; shouldn't every place get you the same amount?
Well so long as they find all the tax credits and deductions that the taxpayer is eligible for, then yes. But some may not.
Software can also be poorly written. For example, when I tried H&R Block last year, it minimized federal and state returns separately, which can lead to the situation that I faced where I could reduce my federal tax liability by taking the lifetime learning credit, but I would actually increase my Georgia state tax liability by more than the lifetime learning credit benefit (lifetime learning credit is 20% of educational expenses, whereas I could take a 15% tax deduction on my federal taxes, and because that was an above the line deduction, it would lower my AGI - which GA uses as the starting point for their AGI - so I effectively also get a 21% tax deduction on my state taxes. So 21% > 20%, I should take the tax deduction (though admittedly, the difference is just 1% of my education expenses).
The software was strictly speaking still correctly written. It just used the wrong optimization criteria (minimize federal and state separately as opposed to federal+state).
I'd imagine this could also occur if your state forces you to itemize your deductions on your state returns if you itemize on federal, and the only thing you were able to itemize on federal returns was your state taxes. It'd have to be pretty extreme though.
There may exist other situations where this can occur.