What David said –and I'd pay particular attention to his final sentence.
YT, et al take whatever you upload to them and re-compress it to display at different sizes. In the process they "throw away" some of the info in your already-compressed movie. The You Tube preset in FCP encodes with a bit rate of 10 Mb per second. The Apple Device 720P preset's bit rate is 7 Mbps, or 30% less. Perhaps the Apple engineers anticipated the additional compression after uploading and built in a bit of a sushi to preserve quality? Whatever the reason, I'm sure the choices were made only after a lot of testing.
If you want to experiment (test) lower bit rates, get Compressor or MPEG Streamclip, wherein you have far more control over file size/quality tradeoffs than are available in Final Cut. And if you use Compressor you could download the X.264 encoder, which is particularly adept at creating high quality output at smaller sizes.
Final thought: pay a visit to broadbandreports.com and run their speed tests to see whether your ISP is delivering the kind of upload speeds they are advertising.
Good luck.
Russ