Ok there are a couple of obvious possibilities.
First you should use the UNIX directory seperator and not the DOS seperator. Remember this is PHP and a \
in double quoted string literals is an escape character.
So first try
browscap = "C:/wamp/bin/php/full_php_browscap.ini"
Secondly, and this is the most likely issue, there are 2 php.ini files in the \wamp\bin\php\{phpversion}\
folder, one called
php.ini - which is used by the PHP CLI ( Command Line Interface )
phpForApache.ini - which is used when running PHP via Apache
Make sure you have updated phpForApache.ini.
If you use the WAMPServer menus like so wampmanager->PHP->php.ini
it will automatically open the correct file for editing. I would guess this is what you have done wrong.