For anyone interested, the following will summarize in maximum geeky fashion most of what I've learned after playing around with hydro vs. refract measurements over the past year or two. I don't claim to fully use all the correct technical terms, I am not a very good engineer or mathematician, but I did play one in college a long time ago.
I have done the same as
@Silver_Is_Money, I have a spreadsheet that compares all the formulae side by side. My spreadsheet includes an error calculation, which I can then use to determine if any formula consistently gives a result that is a little high or a little low compared to a hydrometer reading, and if so, I can normalize(?) or employ noise reduction(?) on the calculations going forward -- I believe this is similar to Dolby noise reduction (for you music listeners out there), and like calibrating your hydrometer in plain cool water, like if you know that your hydro is always high by 0.002, to calibrate then you can just always subtract the 0.002 from every reading afterward to get the most accurate readings. I treat each refractometer conversion formula the same way -- if a formula always gives a calculated result that is 0.002 too high vs. hydro, then I just subtract it off the same way every time forever. That way I am eliminating the permanent known part of the error for ultimate accuracy of each formula and comparing apples to apples, as opposed to concluding anything like "well such-and-such formula is always too high by exactly 0.006 points therefore this formula sucks" -- that wouldn't be right in my mind, because if it is always off by exactly 0.006, then I can very simply do a subtraction, just like calibrating a hydrometer, to get a very accurate result with the refractometer conversion calc. If precision is excellent but accuracy is a little off, not a big deal, we can fix that very easily.
As I said, there are five formulae in total that I am aware of. Sean Terrill and Petr Novotny have two each, linear and cubic. I still find the "Old Cubic" (with original source unknown (at least by yours truly)) and both of Novotny's formulae to be more precise AND more accurate than both of Sean Terrill's. No offense to Sean, as he is a great dude, has done a LOT of great work for the homebrewing community over the years, and I wish him nothing but the best. I just think his numbers are slightly less precise here. But still I think they were the foundation of Novotny's work as well, and for that he deserves great credit.
For what it's worth, myself and others are finding that the default "wort correction factor" of 1.04 reported by Terrill might not be the best average default, and a better default might be closer to 0.99-1.00, i.e., not much "correction" needed at all whatsoever. However, this factor does vary from gauge to gauge, and you really need to run a few comparisons on OG (yes, OG only) to determine your own correction factor. Play around and see what works to match your OG measured with hydrometer vs. Original Brix with refractometer. Once you figure that out, you can use a refractometer conversion calculator to easily get accurate results within 0.002-0.004. Ultimately, if/when in doubt, a hydrometer will always be the most precise you can get. But the five formulae we have here can get you really really close, IF you know your correction factor and IF you calibrate your equipment regularly.
EDIT: Actually what I think I'm really doing is something called "linear regression". I understand the concept but I think I've been doing it manually instead of with fancy automated calcs. Whatever or however, I can tell you that it's working well, as the average (mean?) errors for the five formulae currently range from 0.0006 to 0.0029 for the past 7 batches, so, like I say, within 0.003 or 3 gravity points, versus actual calibrated hydrometer readings. Not perfect, but pretty dang close.
