Certainly one of the stickiest issues in book collecting. I was pleased to see that someone wrote in with this same question to the March 2013 issue of Firsts, so Robin H. Smiley was able to tackle it at length.
I won't repeat all of Mr. Smiley's work here (the letters page my favourite part of Firsts, so I'd feel guilty), but he refers back to 2002 article by Ken Lopez which states that "in general, the more writing by the author in a book, the better".
Mr. Smiley concedes that not all collectors would agree, and many prefer signatures alone over inscriptions to total strangers. However, he says that, over time, "inscribed copies to tend to bring higher prices" (reassuring, as I recite this little fun-fact quite often). Mr. Smiley gives two reasons for this: inscriptions are harder to forge and inscriptions bring additional 'charm'.
I would add my own note of caution to this - I think contemporary authors are now more available to readers than they have been at any point in the past. For earlier generations of commercial fiction, inscribed copies seem to be the only available signed copies - the alternative often being 'flat-signed' short runs or limited editions. More recently, with authors more accessible and signings more frequent, it would seem that copies signed - in some form or another - are less rare. So why settle for a signature for someone else when it could be simply signed? More on this below...
Mr. Smiley goes on to extrapolate an entire hierarchy:
1) Association copy (by this, we mean "inscribed to someone with a personal connection to the author")
2) Inscribed to a stranger
3) Signed & dated
5) Signed on special, tipped-in sheet
6) Signed bookplate (he adds that, if the bookplate itself is valuable for some reason, this could be higher up)
I like how this is all consistent to a single definition of value (in this case, "author involvement"/proximity), but, thinking about my own collecting and shopping decisions, my personal order would definitely be: 1 / 4 / 3/ 2/ 5 / 6.
Unless the date is meaningful (e.g. Halloween, the Ides of March, the book's launch date or before launch date), it actually limits its value to me. I'd rather the plain ol' signing, as it makes the book more... universally appealing.
Similarly, a book inscribed to a stranger has virtually no appeal to me - at least, very little more than an unsigned book. If anything, I've always found them kind of tragic. "To Eloise, who never read this book." "To Chester, who died, and no one else in his family reads." "To Mark, who waited the appropriate amount of time before ditching this at the nearest Oxfam." Etc. At best, a book inscribed to a stranger is a reminder that the book is not mine. An association copy, of course, has a wonderful historical glamour to it. An inscribed one? Not so much.
Clearly I am not feeling the charm of the inscribed copy. But, again, I think it is because my collections are biased towards contemporary literature. But even then... I can think of several recent shopping decisions involving deceased authors where I've passed over inscribed copies in favour of unsigned ones.
And, of course, Mr. Smiley is only talking about a sort of objective worth. If you're considering a book's value to you personally, you have to add a 7th option: inscribed to you.
That's really tricky - imagine the scenario:
You have two copies of Joe Abercrombie's The Blade Itself to choose from. One is inscribed to you. The other is inscribed to his editor, Gillian Redfearn, with a 'thank you', a few in-jokes and dated before publication. Does it mean I have cripplingly low self-esteem if I'd rather the latter? And I'm just... well, not sure I would, but, damn, I'd be tempted.
Obviously design your own nightmare scenario as you see fit, but you can see the issue. For me, it collides two (extremely similar) types of value: personal history ('autobiographical', to quote High Fidelity) and objective history. I will appreciate the book inscribed to me, as it is as mine as is possible. But everyone can appreciate the other, and it is an important artefact in its own right.
(Of course, even those are variable depending on the author. I'm a lot closer to, say, Den Patrick than Joe Abercrombie. In that situation, there's no question that I'd keep the book signed to me over anyone else. But that's because the maximum biographical value is greater than the maximum historical value. Lord, this is tricky.)
What about you? If you had to put the 7 levels in some sort of order for yourself, what would it look it?