In my opinion, if you can afford the extra cost of the PSR-E463, I would absolutely purchase that keyboard over the PSR-E363 if you are wanting something to grow with you and be useful for a long time. I have one of the E463's predecessors, the PSR-E433, and I have been very happy with it for over six years (though it may have developed a defect -- I'll post about that in another thread), and I have been playing keyboard for over 40 years.
The live control knobs, and their related features such as filter, envelope generator, and DSP, give you synthesizer-type control over the sound with the ability to turn the preset sounds of the keyboard into completely new sounds that you can store in registrations, keeping the keyboard interesting year after year. The E363 is a good keyboard, but this control over the sound gives you far more flexibility than what you would get in the E363.
The volume of the keyboard should be fine for a party in a house, but I would guess that larger venues might require an external amplifier and speakers.
I am pretty sure that the E463 has keyboard educational features, as I know my E433 does. In fact, I believe the "E" in these model numbers refers to Educational.
As for the music database, I believe you are referring to the built-in demo songs, and I personally wouldn't put much emphasis on that. These are just songs that the keyboard can automatically play to show off its styles and sounds. Now, I believe the E463 does have a different feature that is actually called a music database that you can use to easily configure the sounds and styles of the keyboard to optimally play (in Yamaha's opinion) over 300 songs. I know my E433 has it, but I haven't used it much. I'm not sure if the E363 has it or not.
Another important difference is the number of registrations. A registration is a memory that stores all of the main settings of the keyboard, including the sounds you have selected, any changes you have made to those sounds (octave, filter, envelope generator, etc.), and the style you selected. Being able to store these settings in registrations allows you to easily and instantly completely change the sounds and settings of the keyboard while you're playing a song, making it easy to change the overall sound at the touch of a button, such as when going from a verse of a song to a chorus or any other time you'd want such a change. Registrations are also very useful for quickly changing the sounds and settings between songs. Imagine that you're playing live -- being able to quickly change the sound and style settings (using registrations) makes it easy to play one song after another without having to take a lot of time manually changing these features between songs, so that you have much less "dead air" between songs. The E363 only has 10 registrations, whereas the E463 has 32, which is a significant difference.
I will finally point out that, based on how Yamaha has updated these keyboards over the years, I would expect new versions of the E363 and E463 in the not-too-distant future, but there has been no official announcement from Yamaha, and Yamaha does seem to be changing their product-updating schedule somewhat, so we don't have a precise guess as to when the next generation versions of these keyboards will be introduced. I only mention this to point out that, if you are not in a hurry, you may want to wait a few months to see if there are any announcements. But otherwise, the E463 is a fine, feature-packed keyboard -- especially for the price.