I own a D5300 and am quite happy with it, and have siblings with the D3200. Here are the main differences I see:
1) Price. The D3400 is normally about 100USD less. You will be that much ahead when it comes to buying additional lenses, batteries, filters, memory cards, etc.
2) Battery life. The D3400 has a slightly better battery life. It appears to be 1200 vs 600. It actually isn’t much different – as Ken Rockwell explains, the better battery life rating is because of a weaker on-camera flash… A more accurate comparison would be 700 vs 600. Also note that battery life is greatly improved by buying a spare battery and carrying it in your pocket when needed. 🙂
3) Screen. The D5300 has a tilt-swivel screen.
4) AF points. The D5300 has more cross-type AF points. This is an advantage is you want to use a focus point that is not in the centre of the picture.
5) Burst mode. The D3400 can shoot faster and for longer. It will shoot at 5.1 FPS vs 4.0 FPS and has a 12 photo buffer vs 4.
6) ISO. The D5300 actually has less iso noise at high iso’s, even though the D3400 can be jacked up higher. Whichever one you get, you will probably take a few pictures above iso 1600 and then decide that it isn’t worth going higher than that.
7) Auto-bracketing. The D3400 does not have any auto-bracketing.
8) External mic jack. As you noted, the D3400 does not have an external mic jack. I have never actually used it on my camera, and the built-in mic is not great. If video is really important, I would get an external sound recorder and sync the sound in post. But neither camera is really made for pro video.
9) Age. The D3400 is about 3 years newer.
In my work (real estate) the tilt-swivel screen and auto-bracketing are really big advantages. Otherwise, I don’t think they are a big advantage to most people.
To sum up:
D3400 advantages:
Better price
Better burst mode
D5300 advantages:
Better auto-focus
I hope this helps!