Low ISO JPEG
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.
High ISO JPEG
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.
ISO 100 JPEG
Low ISO JPEGs look pretty sharp.
ISO 200 JPEG
The image stabilization in the new lens doesn't seem to be as effective as I'm used to.
ISO 800 JPEG
In reasonable light, the D3300 fares OK at ISO 800.
ISO 800 raw vs. JPEG
The default settings tend to push the contrast and clip shadows for JPEGs.
ISO 1600 JPEG
This is pretty good for an inexpensive dSLR.
ISO 3200 JPEG
This is still quite acceptable at ISO 3200.
ISO 6400 JPEG
The detail resolution at ISO 6400 is quite good.
ISO 12800 JPEG
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.
Color
The camera renders colors relatively accurately.