It all depends on what sorts of photographs you do/will take.
For
. Images in good light at ISO 100
. Macro of small objects
. Low weight
. Minimum number of buttons and controls
. Rock bottom price
D3300 wins.
For low light, professional features, lots of buttons and dual cards D810 wins. As you asked is it worth 3 times the price? Not if you have no need for 36MP FX or low light capabilities.
I've been testing my ISO range and the D3300 performs well enough up to 800. At least for what I do. Sure I see some noise appear at 100% but the way I process, it is of little importance. Higher than 800 not so much.
These days I hardly ever shoot at 100. In macro too often all from the waist down is in shades which requires some upping the ISO but I even use it in full sun. There's too little difference between the shots to not benefit of the DOF increase.
If I'd be a professional, the D3300 would probably lack here and there but for a hobbyist, it's the right stuff.