Typically NONE, in my experience. The only external difference is the three piece back. There may be some support differences inside, but I doubt if they are major tone affecters. I own one of each model and cannot tell much difference in sound. What difference there is, I attribute to age, uniqueness of the individual guitars, etc.
It was my understanding that the D-35 evolved as a way to incorporate back pieces from D-28s that did not pass the fit test. The D-35 shape gives them a chance to cut the piece again. That may be "rumor," as I am not an insider at Martin.
Or in this case, comparing one apple to one banana, LOL.
Most of us are in that position. How many guitars are available for us to "test?"
I thought Martin's marketing strategy was brilliant. When faced with dwindling rosewood supply, they came up with an idea to use pieces that were too small for a D28 or a D21...use a three piece back. Realizing people would feel it was inferior to the two piece back, they put extra binding up the neck and used lighter bracing and charged more for the 35 series.
The lighter bracing was intended to give more bass and treble response. With a scooped sound, the guitar could have less volumes in the frequencies that would compete with the vocals, making it a favored choice for solo performers.
Ensemble players...especially those in bluegrass groups, still tended to favor D28 and D18 models which needed a full range of volume to compete with banjos and fiddles. Then, to give a wider range of responsiveness, Martin reintroduced HD28 models featuring scalloped braces like vintage models.
Although every piece of wood has its own personality, there are usually common characteristics to the designs of straight bracing, lighter bracing and scalloped bracing.
If you are buying new, play about a half-dozen of each (across three or four stores) and buy the one that "fits your hand and ear." Don't worry about which model it is. If it's the right guitar for you, it will remind you of that for MANY years. Remember also, that most new guitars require a "setup" to be just right for your playing style. That costs about $75 and is worth every penny. Small adjustments can work wonders with playability.
P.S. If you can possibly afford about $500 more, look into a D-41. They are much richer sounding, and the prices are quite depressed right now. Remember to dicker on price. It's like buying a car. The dealer starts about 20% too high most of the time.
Gregory, it might not be correct to conclude that there is no tonal difference, but it may take some time and critical listening to hear the differences. It is also important to consider the other variables folks have mentioned here, such as your preferred style of play, fingerpicking vs flatpicking, rhythm accompaniment vs lead, solo performance vs small group vs larger ensemble and other instruments in the mix, etc. I'm an old dude, and the ideal sound of a guitar I carry in my head has changed or become refined over the years. I have enjoyed spending time in many music stores trying to develop my ear to hear the differences in the voices of various guitar models and then attempting to memorize the sounds for later comparison with other models.
I would strongly second Alan's recommendation even within a single model that you check out a number of examples. Guitars are organic entities, not cookie-cutter identical replicas. A friend of mine, knowing he was in the market for a D-28, went to nine different music stores around the San Francisco Bay region before he found the one that felt and sounded the best to him. He remains totally satisfied with his selection. However, when he heard my D-35, he was quite taken with it and began checking out D-35s at a local store. He came back disappointed, because he said none of them sounded like mine. My D-35 is over 35 years old, so that might suggest to you how age of the instrument is another variable. Plus, it has been optimized by John Mello, who is featured in the most recent issue of Acoustic Guitar. He is a luthier who really knows his craft. That speaks to another recommendation that Alan makes out getting a proper set-up.
Ed Rhoades' comment about the scooped out sound of the D-35 reminded me of an interview I read wherein Tony Rice said he evaluated guitars by the tonality of the interior two strings, the third and fourth string.
I think all of us in this group love Martin guitars for the rich warmth of their bass. I enjoy bluegrass music, and I get a thrill out of hearing a ringing treble, as well. That prompted me to recently acquire another Martin dreadnought which Martin calls their America's Guitar. That name doesn't tell you much, but it is essentially an HD-28V with a Madagascar rosewood body, adirondack top, with forward-shifted scalloped bracing. Now I finally have a guitar that delivers the sound of a sledgehammer striking a steel spike when I hit that bluegrass G chord, but that is not a quality that would be important to folks playing other kinds of music.
The search is part of the fun. Enjoy yourself.