I've grown to like the HE-560 a fair bit, but I don't find that they do anything better than the HE-500. Maybe detail retrieval? The HE-500, by contrast, has better bass extension, more coherent mid range, smoother treble, and is just overall more musical. That being said, the margin between the two headphones is pretty small. The HE-500 isn't so much a drop-in upgrade to the HE-560, it almost sounds like it's the newer revision of the HE-560.
Your mileage may vary of course, but I would absolutely recommend the HE-560 to someone who can't find an HE-500, but since you do have one, hold on to that headphone with both hands!
I don't have experience with the HE-560, but I did have the HE-400i at one point and I think they sound fairly similar to the HE-560, but the HE-560 is more balanced and has a wider soundstage than the HE-400i.
That being said, I think the HE-500 has better extension and and more balanced sound than the HE-400i, but only just. Further comparisons show they come from the same house sound with small variations.
I think you should keep comparing the two yourself with different music and see which you'd prefer to keep, or keep them both why not lol. Personally, I would definitely keep the HE-500 since I find their midrange very similar to the HD650, but presented slightly differently - a little more energetic if I may say.
Other than that, from what I've read, they're fairly similar in sound that keeping both is redundant and you should keep which gives you more pleasure in listening.
I've owned the HE-500, HE-400i, MD-4XX, HE-5LE, HE5SE, HE6SE - and heard the HE-6, Sundara, 400s, and the 560 - pretty much all the round form HFM cans of the past 11 years.
For my money, the HE-500 nestles in #2 after the HE-6, and ahead of the HE6SE (Adorama - read about my issues) and 560 (v1) - the next two best.
The HE-500 is amazing in how much a mid centric can it is - and yet the bass and treble are both obviously excellent in their own way. It needs 2 wpc at 50 ohms to get the best out of it.
It along with the HE-6 are among the most modded cans of all time - not because the driver stinks, but because it is superb, but the stock cable, headband, rear screen, and pads are all haphazard/low quality.
I've got the HE6SE, HEX v2, HD-600 also and the 500 is still getting 50-70% of my listening.
The 560 is clean, has a bit of bite around 9 kHz, quite nice, just not a 500. Let's try this way if the he-6 is a 97/100, the 500 is a 94/100 and the 560 is an 88/100 and an unmodified 4XX is a 78/100. The 500 and 6 with mods are a lot closer to real music than other round form HFM no matter what u do to them. The Arya is better outside bass impact then the 6. But even used - Arya (~1100) and HE-6 (~900) cost a lot. The 500 is less than half that (~400).