The D3300 preserves detail in JPEGs pretty well up through ISO 1600, though you can start to see some degradation in shadow areas at ISO 800.
ISO 3200 still looks OK in bright areas, but by ISO 6400 there are quite a few visible artifacts. I wouldn't recommend shooting ISO 12800 or higher JPEGs unless you're planning to keep it scaled down.
Low ISO JPEGs look pretty sharp.
The image stabilization in the new lens doesn't seem to be as effective as I'm used to.
In reasonable light, the D3300 fares OK at ISO 800.
The default settings tend to push the contrast and clip shadows for JPEGs.
This is pretty good for an inexpensive dSLR.
This is still quite acceptable at ISO 3200.
The detail resolution at ISO 6400 is quite good.
As long as you're scaling down, the camera handles high ISO sensitivity/low-light situations relatively well. There's some unavoidable hue shift as the blue noise becomes prominent, though.
The camera renders colors relatively accurately.