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.
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.
I just opened allCountries.txt[1] in ~36 seconds on my MBA and vim scrolls through the file smoothly. 8 256 007 lines taking up 960MB.
[1] http://download.geonames.org/export/dump/allCountries.zip