I must respectfully disagree that the main difference between a PSR-E463 and PSR-SX600 is the sound quality. I'm not saying that there is no improvement in sound quality, as I'm sure there is, but I do not believe it to be as dramatic as the price difference implies, and I believe the PSR-E463 can sound very good -- especially with proper use of effects like chorusing and reverb to fatten up the sound. Add some external amplification and speakers, and it sounds even better. The OP mentioned a flute sound, and I just happened to be doing some experimentation with the flute sound recently on my nearly 8 year old predecessor to the PSR-E463, which is my PSR-E433, and it has a "Sweet Flute" sound that is just amazing.
So, what do you get for the price difference when moving from the E463 to the SX600? After all, the SX600 costs about three times as much as an E463. Here's a partial list...
Hundreds of additional sounds
Hundreds of additional styles
Dozens of additional chorus, reverb, and DSP settings
80 more notes of maximum polyphony
Number of registrations limited only by available memory in the keyboard, instead of just having 32 available registrations
Style creator
16 track sequencer, instead of 6 track -- and with more features
Additional auto-accompaniment modes, as well as 4 style variations instead of 2
Master compressor
More EQ settings
Multi-pads, which are not available at all on the E463
Modulation wheel control
More settings for the live-control knobs
More power for the built-in amplifier and speakers
There are likely even more, but this gives you a picture of the many additional features included with the SX600. Granted, you can argue that things like the compressor, EQ, and additional DSP effects, as well as the additional polyphony available, all relate to an improvement in sound, and that would be true. And the additional onboard amp/speaker power may alone justify the SX600 (or an even higher-end model with more power) if the OP is not using external amps and speakers and is using it in a larger church. It just depends on how he intends to use the keyboard, and based on his original post, these features don't seem all that important. If he is mainly holding down a 3-4 note pad chord with his left hand while playing a single note melody with his right hand, then I doubt he will notice a difference between 48 and 128 note polyphony.
Another consideration is whether he thinks he may use this additional functionality in the future. If so, the the SX600 could still be the better choice. Otherwise, it might even be worthwhile even to check out the E373 (or EW310 if a bigger keyboard is important). You lose things like the live control knobs and USB to device port, but those features also do not sound very important to the OP. I have no direct experience with it, but it appears to have quite an improved sound when compared to previous E300-series models, and now includes dozens of DSP effects. However, it still only has 9 registrations, which could be quite limiting if he plans to store combinations of sounds in registrations.
Of course, depending on how soon the OP needs to buy this keyboard, it might be worth waiting for the long-awaited PSR-E473 and PSR-EW425, which still involves quite a bit of speculation, but may not be that far away since a leaked picture of the EW425 is out there and is discussed on another thread on this forum.