The difference is that I have never seen eudan(n) in my life and I would be baffled if I did. Dwelly says nothing about them except to cross-refer to aodann. AFB copies words from Dwelly but has failed to indicate the subsidiary nature of these words. Mark does not mention them. Any other dictionary that has them might have copied them, directly or indirectly, from Dwelly.
Stick to aodann. D
This sort of question is almost impossible to answer. I have a book which will show me which geographical areas had which pronunciation in the 1950s, when most people spoke the dialect that had been used in that area for centuries. But two major things have happened since then. One is that many people are picking up Gaelic from non-local sources, such as the BBC, teachers that come from different areas (there was no Gaelic teaching in the 1950s) and even Duolingo. The other thing is that these different areas have been subject to very different changes in the number of Gaelic speakers, and the relative numbers will depend on whether you count people who are first-language, fluent or learner.
I did look up ceart in the Survey of the Gaelic Dialects of Scotland, as they had no examples with a slender rt. It was a bit of a struggle because they use non-standard symbols, but a small majority had some form of sibilant (s-like sound) before the t. However I was very surprised that none of the 207 pronunciations has the /ʃ/ - the sh that I am assuming you are referring to, and that I thought I used. The most common was ṣ which is /ʂ/ in IPA. This is a retroflex s - curl the tongue up to get the tip as far back as possible then try to produce as s. I think this may be what I am doing, at least some of the time without realizing it, but it is a subtle difference.
I listened to all the recordings available here. Unfortunately they are all by one person. Nevertheless, he is definitely pronouncing the aodann goirt differently from all the others, so well spotted. All the others have some weak sibilant before the t but it is hard to make out. And they all have a /ʃ/ after the t, so it is not "gorsht" as you have heard and I say, but "gorshtsh". This is of course the difference between the slender t in goirt and the broad one in ceart. There 'should' be the final /ʃ/, but I never do, and I don't think many people who put the first sibilant in put the second one in as well. It's just a pity there are no slender examples in the SGDS.
So I think his "gorshtsh" is quite unusual. It could be that the way he speaks in front of the microphone when recording pronunciation is not the way he speaks normally. D