I guess it depends. I have 3 computers at home. The company one (highest security settings) always has problems with KLM, not so much with AF. It runs IE8.
My home pc runs IE7 and has medium security settings. It goes to hell on KLM about 75% of the time (regular & award booking and account information). AF works fine. Firefox or Chrome make no difference.
My travel PC runs IE7 with very low security settings. It works about 75% of the time. The 25% it doesn't work is - obviously - always during OLCI...
It is a mess and most travelers will have encountered problems since even the KL CSD admits the problems exists but IT is holding them off.