Not sure I can answer the original question, but can relate an recent event that would say indicate it is both. A coworker had come back from Prauge with some color prints (35mm) and she commented they did not look right, and could I look at them. Looked at about 4 or 5 and set them down and told her it was one of the worst printing jobs I had ever seen, the negatives were fine, but who ever the Yo-yo was that was running the machine at the quick lab did not care about the final image. My guess was, the negatives were scanned and digital output to regular photo paper. Now the scanning way horrible, the people in each picture were either long and thing (a problem I would like to have) or short and wide (a problem I do have...at least the wide part). Then to make matters worse the color was off, and it appeared that either the edges were not exposed at all or machine was out of alignment.
So, in this case it was the process that was most important, but that will not always be the case.
I think that it is the image not the process debate has many levels of answer. I stopped freelancing for a local paper because I did not want to buy a digital SLR, for what little I made freelancing I could not justify the cost of a digital system. The paper no longer has a darkroom, but I think they have a scanner, all of the work is turned in on digital cards. For the photo editor process very much matters. An art director may insist on a digital file and may want the original digital file, not a file from a negative scan.
But if I were in the market for high end prints I want prints that I know will last and so I can hand them down to my son and grandchildren, at this point I just don't trust digital for archival quality (not to mention overall quality). On the other hand what is the point if the final image is archival but does not grab me?
On a more personal note, shooting for me, myself and I the process matters because I don't like working on computers for pleasure. I use a computer all day long and I don't enjoy digital stuff at all. If all of the film and paper goes away I don't think I would buy a digital system, it would not be any fun, I enjoy the wet process.
As one of those who feels that the image is paramount, I thought I should respond...
For one thing, "Does the process matter?" is an open-ended question, and the "answer" - if there is one answer, depends on the context.
As I said, the process is very important to the person engaged in it - ideally you have (or are learning) a process that you know and love and you can do great things with it. (That said - nobody knows everything, so a degree of open-mindedness is a good thing). I would never recommend to anybody that they arbitrarily abandon a process for which they are so evidently passionate.
However, just because a process is right for you doesn't mean it's right for everybody. Different people are comfortable with different styles of cameras, which entail different styles of working, and different people have different desires for the "end product". A handmade print is only one of many possible results from a photographic exposure.
Just as you want to be respected (or at least left alone to do it your way), other photographers deserve the same consideration. There are so many choices, so many decisions in the process - there is no one "right" way, but I've encountered many smug and judgemental photographers that thought anyone "serious" about photography would, of course, be using, "X" brand of camera and "Y" brand of film - this sort of attitude started long before there was digital to kick around and it has always bothered me.
I think another interesting issue that this question brings up is the idea of whether you see a photograph as an object, perhaps decorative, or something much more - like a communication device for ideas, emotions, thoughts, perceptions, viewpoints, etc. There are those who seem to be comfortable comparing their photos to coffee mugs, coffee tables and figurines. I'm more comfortable with a comparison to the short story, or essay. They can start as pencil on paper, be further developed on a mechanical typewriter and edited on a computer. They can then be printed in newspapers or magazines, anthologized into books - the books can have soft covers or hard, or be printed as handsome leather-bound volumes - but all of that is secondary to the words, the content. Good content will transcend any medium... the medium is not the message.
Lastly, if the image is not paramount, are you saying that the process is? That the image does not matter? That it's all about the process?
Food for thought...
Why do we assume there's a universal "right" answer to this question? As this thread has already shown, different people have different values, although most people tend in some degree or another to attach value to difficulty.
Put another way, if the process matters to you, you're right. If only the final image matters to you, you're still right. If you try to impose either on others you're wrong.
I dont't think Aggie's observation about Adams vs. a good digital artist is really a very good impeachment of digital--it's like pointing out that Shakespeare is better than Toni Morrison, and then using that to show that word processors are inferior to pen and ink as writing tools.