Of course Log Horizon is much better than SAO. My elder sister disagree's, but she hasn't even seen Log Horizon yet and she says she'll like SAO better. -.- Anyways, Log Horizon is just amazing and for SAO...I couldn't really get into it, the characters weren't that great and the story wasn't that great as well...I think SAO could've been improved by a lot, but that's just me.
Tell your sister that she has to watch the show before having constructing her opinion. SAO does have better production value, the fighting scenes are gorgeous, the music is just amazing but the story itself is where it falls apart. It had the perfect setup for a story that they ignored a few episodes in and then completely ditched it halfway through the season. It was very, VERY disappointing.
That's why Log Horizon has a better story; It sticks with the original setup for the story and builds upon that. Sometimes the pacing feels a bit sluggish, which is a problem I have with anime in general.