I never had problems with large files on Sublime Text, in fact when vim chokes on those, I open them in Sublime.
Notepad++ does handle those with ease, but only on win, Sublime Text is cross platform.
Vim sometimes chokes on long lines, and very rarely on long files. Both of these are caused by the plugins and settings you have enabled though, not by how the editor works.
If you have a plugin that scans through every line in a file (yes, some are this stupid), a large file will take ages to load. Some syntax highlighters that use inefficient regexes have a similar problem, but with long lines.
You can test this by opening your giant file with `vim -u NONE large.txt`. That disables your .vimrc.
