Not at all. They seem to do well with modestly powered amps like 650-750mw HiFi-M8 which I would call the bare minimum for optimal enjoyment, but the F-35's extra power in balanced mode is very useful - it's like BAM! They really thrive on a 2-watt EF5, or a 3-watt Eddie Current ZDT, or a 5 to 6-watt EF6, like all orthos do.
I would say the treble (and speed) is very stat-like but without the etch or glare of some of the vintage Stax like the SR-Lambda Pro and SR-Lambda Pro Signature (which was much better). The air, ambience and transparency is wonderful with the HE-560. Note - the HE-6 also have a very stat-like presentation, and they competed well with my HE-60 and SR-007 in past listening sessions.
Well, I wanted to say they are both on the same level, with just different sound. But while I still love the HE-500, if I had to pick just one it would be the HE-560, for it's improved speed, detail, sparkle, and soundstage. Note - both phones here are stock, not modded. The HE-500 still have a warm and inviting sound with good detail at the same time, as opposed to a dark and veiled HD650 for instance, and with having both here together I would not want to give up either one.
I thought the original HE-5 were great (with the EF5 amp, or Square Wave XL amp, or ZDT), but the HE-5LE were an upgrade with less recessed mids and a more refined sound, while the HE-500 improved upon that by adding more stable imaging and improved treble. However, I NEVER considered selling the old ones as I upgraded, because I still like the older ones too much. Same goes with the HE-560, they won't get me to sell my older HiFiMan headphones.