I'm confused between Nikon D3200 & Sony HX300. My use will be mostly for home video?

I'm confused between Nikon D3200 & Sony HX300. My use will be mostly for home video?

Neither.

The D3200 is a dSLR.
The HX300 is a bridge camera.

Both are designed to capture digital still images - video and audio capture are secondary "convenience features". Since video (and audio) are your primary requirement, then a camcorder is a more appropriate solution.

If All your video capture is short clips, then you might be OK. In my experience, "home video" also includes kid's school stuff, concerts, and other activities that can require over 20 minutes in a single clip. The bridge cameras and dSLRs in your budget range - regardless of manufacturers all will overheat and stop recording video. Read their manuals. If longer clips are needed, these kinds of cameras will auto shut-off at 29 minutes (assuming you get past the overheating issue).

You are in the camcorder forum. You can ask the same question in the camera forum and will likely get a similar response: dSLRs and bridge cameras are for digital still image capture should not be used as a camcorder replacement. This does not mean their video quality is not good - it is, but they have a different set of requirements and are not camcorders.

Mmjj is right, DSLRS can shoot awesome videos but they do overheat very quickly when shooting vids, i shoot videos with my DSLR, but i shoot music videos and nature which i shoot in small 1-3 min portions, sometimes when am outside on a sunny day i have to stop shoot and let my camera cool down, not very convenient for a live event you will miss important events/shots due to over heating. So if your primary use is home video go get a camcorder. Canon VIXIA HF S30 is a excellent cam for that