Eh... my family is Scottish and I do not think anyone really cares either way. We won in the long run anyways... sort of.
http://en.wikipedia.org/wiki/James_I_of_England
As for the Welsh. There is a great pride in some ways of Edward there. One of the few places that sided with Edward II, Edward I's son, during his deposition were the Welsh. A interesting turn of events I'd say. Of course they revolted against Edward I several times and continued after against several other kings but hey that’s what the welsh do.
The issue with these events is that nations as we think of them do not exist. Wales was a loose confederation of Welsh Princes and other nobles and Scotland was its own kingdom with a complicated and ancient feudal relationship to England. You have a great number of Scots and Welsh fighting for Edward I so it is questionable to look at them as a war of nations or people so much as a war between Edward I and some Welsh Prince or Scottish king.
The Mongols are interesting. Sort of the same situation with Alexander the great takes place. Powerful and charismatic people who make an empire but when they die no one can replace them so it breaks apart.
I agree Edward I achieved a great deal but do not forget that Edward III won 1/3-1/2 of France during the 100 Years War. While most of it was lost within his lifetime, Edward I lost Scotland during his lifetime as well, his only real permanent accomplishment was in Wales where he took the north of Wales as the south was already under the English by his reign. Edward III also really developed the military, legal and social administration in his day and began to establish English as the language of the court (English was to be used so that everyone could understand what was being said) and parliament (Somewhat the same thing but partially as propaganda against the French). Some fairly big accomplishments. He was born November 1312 and died June 1377. He was made king in February 1327-June 1377, a very long 50 year reign-one of the longest ever. He was a soldier, leader, diplomat, and other roles over that 50 years, sadly the last decade with the death of his wife and son really leave his reign on a low note.
Heir of BF
There ain't nothin' girlie about a tunic...