On the face of it, Log Horizon is effectively identical to SAO. It's about players of a MMORPG being trapped in that MMORPG and having to work out how life is going to proceed from here on in. Initially i didn't really pay it much attention because I figured it couldn't be all that different. How wrong I was.
The key differences come down to the peril involved and the perspective. The big peril in SAO was that if you died in the game, you died in real life. In Log Horizon if you die you respawn at the cathedral and people loot your corpse. This means that it no longer becomes a struggle for life and death and instead becomes a struggle to reclaim society and that's where the perspective comes in.
SAO had us hunting for an escape, whereas Log Horizon introduces us to the deep mechanics of how classes and guilds work (something which SAO pretty much glossed over in favour of "the good stuff"). It makes for far less epic battling but perhaps more satisfying battling. The solutions here are never that it turns out somebody had a particular power or that they managed to believe in the power of friendship or any of that; they come through strategy and explaining their approaches.
That emphasis on how things work takes us into the guild and societal side of things and that's where it really takes on a life of its own. Log Horizon lets us see the formation of a society and how it interacts with others and with itself. So far it's all been very interesting. It gets you to ask a lot of socio-political questions and asks you to actually put some thought into how everything around you works on a fundamental level.
It never quite reaches Spice and Wolf levels of economics, but it definitely doesn't pull punches and it manages to do it all while providing plenty of humour, action and fanservice along the way.
So if you liked SAO but thought it needed more substance to it and less hack'n'slash and romance then Log Horizon might be worth jumping into while it's at the halfway mark.