"At large" can be used more generally, for anything dangerous that is still free. For example :
Two lions escaped from XXX zoo yesterday. One was recaptured immediately, but the other is still at large.
It can also be used humourously as in the children's book "
Paddington at Large" which relates all the problems Paddington Bear manages to cause and how they are eventually resolved.
"On the run", however, definitely refers to a criminal hiding from, and being hunted by, the police. It couldn't, for example, be used in the sentence above describing the escaped lion - which is not consciously "hiding" - or in the title of the Paddington Bear book - although Paddington gets himself into a lot of trouble and is humorously "dangerous" in that respect, he's not "criminal" and the police aren't looking for him.
In the context of criminals however, the two terms are interchangeable. Here's a headline from today's press using "on the run":
Strasbourg suspect Cherif Chekatt still on the run while another press report on the same story used "at large":
2 dead in Christmas market attack in Strasbourg, France; gunman still at large