Well I also applied for Chinese and History at both institutions but I also quite sure that I will choose SOAS, although I would not have to pay any tuition fees at Edinburgh University as I am an EU citizen... However Edinburgh's Chinese course has only been running for approximately 18 years or something and what is that compared to the experience of the department at SOAS. Also the year in Dalian is definitely a reason for not choosing Edinburgh as Dalian isnt a really famous uni in China, whereas Beijing Normal University is the best university of China... I dont know much about the flexibility of the History course at Edinburgh but I can guess that you study History in a more general way at Edinburgh as it does not focus on Asia/Africa like the SOAS history course. However I think for someone doing joint honours Chinese and History its very likely to specialize in Asian history, what can be done best at SOAS I guess.
btw I am always wondering why people post these threads("Edinburgh or SOAS?") in the SOAS/Edinburgh forum. I mean of course everyone here will tell you to choose SOAS, as you will mainly find people here, that already study at SOAS or applied for a course at SOAS(what means that they also wont dislike it much...). For the Edinburgh forum it wont be very different I guess..., which is why I would just post it in the modern languages forum or somewhere, where you find students of both unis