There is no point in having both installed.
Winrar can handle the ZIP format plus many others so WinZip is redundant. Besides, compared to RAR ZIP is an inferior compression format. Only reason it still is around is because it is so widely supported. In fact Windows XP and Vista have built in support for the ZIP format, so on those systems WinZip is completely useless.
Out of curiosity, what is your friend's argument for having both installed?