I'm curious as to why exactly did you suggest Avast Premier? I would guess Avast Internet Security vs ESET Smart security would be a more suited comparison. A little nitpicy, I know, but I'm just curious.
I tried ESET smart security a few days ago. And wow, my browser performance was badly affected and videos would hardly load properly.
I haven't tried Avast for quite sometime, though a family member of mine has it installed with no problem last I heard.
Based on that, I would go with Avast. However you might be fortunate, and won't run into any issues with ESET. I suggest you take your time, and trial them before deciding.