If you get either the D7100 or the D5300, you may find you no longer need your 35mm film. The film is about 2x the area of the D7100/D5300 sensor, but it is about
30x the area of the DSC-H200 sensor. And a lot more effort has been put into improving the image quality of the digital sensor than of film in the past decade, so the D7100/D5300 sensor will be very competitive with, if not better than, the film.
Now, the qualitative differences between them:
1. The D7100 has two dials to change settings, the D5300 has one. If you are shooting in manual mode, for example, this means one controls aperture while the other sets the shutter speed. With the D5300 you use one dial, and press the exposure compensation button to change the aperture. I find two dials much more convenient.
2. There are also more controls which can be set by pressing a button and turning a dial on the D7100, so you never have to take your eye off the viewfinder.
3. The D7100 has a autofocus motor built in while the D5300 does not. The D5300 will only autofocus with AF-S lenses, while the D7100 will autofocus with any AF lens. There are some excellent AF lenses which have not been updated to AF-S lenses (200mm f/4 macro, 105mm or 135mm DC lenses are two).
4. The D7100 has two SD card slots, the D5300 has one. If you are shooting a once-in-a-lifetime event, you can have two copies of the pictures to insure against one card getting corrupted. You may not want to do this all the time, but it is a nice option.
5. The D7100 built-in flash can be the commander to control Nikon Speedlights remotely, which gives a lot of options especially for portrait photography.
6. The D5300 has an articulating screen.
7. The D5300 has built-in GPS and WiFi.
Overall, I think the D7100 is a better camera for many photographers.
For a little less than the Costco price, you can get the
D7100 + 18-140mm lens. If you look at your better pictures with the H200, how often are you going past 200mm (35mm equivalent)? And how often are you in the 70-200mm range (35mm equivalent)? If you are not going past 200mm, but are often past 70mm, then the 18-140mm lens gives a good range in a single lens, rather than needing two lenses.
If you get either the D7100 or the D5300, you may ... (