Actually it's very simple. The difference between them is pretty much the same as neglect and ignore.

没有什么区别，不理口头说的比较多。

我同意Alice和Monkey的观点，另外做点补充： 1 无视： ‘视’是看的意思，无视就是不看，也就是不把什么放在眼里，根本不考虑，当不存在。 例如：你不能无视她的存在，你要多关心他。 这个问题一直都存在，你不能 无视它，要想办法解决它。 2 不理：不理睬，不理会，不在乎，不当一回事。 例如： 哥哥不理我。（不和我说话，交流） 我才不理那些闲话。（不当一回事）

good question. in fact, 不理 is NOT a word. :) I believe that even lots of chinese haven't recognize that 不：dont 理：理会、搭理 so 不理 is the nagation of 理会 and 无视 is a word. so 不要理会 = 无视 so we can say 你可以无视他 but we dont say 你可以不理他 i know some chinese think 你可以不理他 is correct, but if u let them to express the same thing, they will say: 你可以别理他 or 你可以不要理他----------------------because 别 = 不要

First, 无视 is more formal, more used in writing and stronger in tone. Second, 不理 can always be replaced by 无视, while 不理 can't replace 无视 in 'set phrases'. For instance, we can say '别不理他 Don't ignore him' and we can also say 别无视他。 But we can only say ‘别无视法律 Don't defy the law', ‘不理法律‘ just doesn't exist. In order to differentiate them, you can consider 不理 as ' pay no attention to' and 无视 more like 'defy, disregard' in English.