Eye Appeal Vs Grade.

first, I don't claim to be a pro at grading, or even good at it most of the time, but I can tell the difference between VG and AU...

plus I refuse to buy into the whole "pay to have someone grade a coin that I could grade myself" (I'm not collecting MS coins),

so I choose eye appeal, 100% of the time

For me, it would have to depend on how bad (or detracting) the problem is.
If the coin is holed, harshly cleaned, severely corroded...forget it.
Coins that have these issues have 0 eye appeal to me, regardless
of grade.
I have many coins in my collection that are problem coins but still retain nice eye appeal.
My vote, it just depends.
Beauty is in the eye of the beholder I guess.

If it's common enough that I could buy the low-grade version elsewhere reasonably easily and cheaply (say under $10), then I probably choose the AU and next week buy a VG-10 example elsewhere (and very possibly trade the AU away for something else). If there's not much of a price/availability difference up to XF-AU either, I buy that instead (and might choose on eye appeal - see note below).
If it's uncommon/valuable enough that I could send the AU coin to be slabbed, then sell the newly slabbed AU-50 coin on ebay, and still get a decent profit (say $50 or more), I likely choose the AU, proceed to do just that, then buy something I actually wanted but couldn't afford (for $50, probably a Morgan dollar, but there are several other possibilities). If it's already something I wanted but couldn't afford (such as, I don't know, a Siberian kopek), I probably choose the VG (but see later note on eye appeal).
A few coins are either so ridiculously common or have so much bullion value that they cost pretty much the same in VG and AU. If the first (and it doesn't fit in the previously-mentioned "very cheap" category), I choose depending on eye appeal (which might not necessarily be the VG coin); if the second, I choose the VG (because silver with green spots is really ugly, and corroded gold is so unrealistic as to be next to impossible... and probably still really ugly) and then gloat about having such a valuable coin.
Several designs actually look much better to me in VG than they do in AU (in fact I think Morgan dollars are an example); then I certainly choose the VG. Some more designs are usually missing some very important details (date, type, mintmark, etc) when worn to VG; in this case I would probably choose the VG if it somehow still has them and the AU otherwise. Yet other coins (especially commemorative) are actually more common - or occasionally even less valuable - in AU than in VG; in that case I probably choose the less common/more valuable VG version.
...I probably missed a few more specialized cases; but generally, if it doesn't fit into any of the above-mentioned situations, I probably decide on eye appeal - which, as said above, might not necessarily be the VG (for example, if the design has enough beautiful details that show up in AU but don't in VG, all the other detractions involved might not actually detract from the eye appeal more that missing these details would).

Eye appeal for me every time. That said, it would be unusual for a poorly graded coin to have great eye appeal if placed beside a highly graded one. The choice between the two is probably better discussed for grades that are similar, i.e., a VF+ graded coin versus an EF coin with a huge ding or holed etc.

Eye appeal.

An absolutely, no-question coin in any grade beats a "coin with questions" in any grade day.
IN MY BOOK. You may read a different book.
I am happy to see a number of you appreciate eye appeal.

Having said that, a real,correct choice cannot be made without actually seeing the two coins.

Neither as they both sound nastaayy!!
Perhaps AU50 as its a better grade, be amazed how such a high grade piece could be corroded and dirty unless buried in a pile of salt water sand or something.

Eye appeal wins every time for me