The D7100 is at least 2-stops better in bad light. That is huge if you shoot action indoors. The D300 has the same sensor as my D90, which looks OK to about ISO 1600. My D7000 is good to about ISO 4000, and usable to about ISO 6400. The D90/D300 is mush at those ISO's. Also, the 24MP files from the D7100 can be cropped much deeper and cleaner than the 12MP files from the D300.
The D7100 gives you 6FPS at 14-bit/24MP, and 7FPS at 14bit/16MP in crop mode. The D300 is 7FPS at 12bit/12MP, without the grip. To me, that is advantage D7100. IMO, unless you drive nails with your camera, "build quality" is a wash. The D7100 is weather sealed, and mostly a magnesium body.
All of that said, if you don't crop, and don't shoot action in low light (or anything above ISO 1600), then all of those "handling" advantages of the D300 may be meaningful enough to sacrifice the dynamic range advantage of the D7100 for a D300 and it's lower price.