Both are tuned different as per my knowledge. 650 is warm and mid focused. 560 is neutral bright kind of tuning. (Havent heard 560 but had a 6xx before which is similar to 650) hd650 need hell lot of power to get the maximum out of it, otl tube amp prefered. 560 is easy to drive compared to 650. If you get the 650 then you need to spend more on amp but you can drive 560 to good level with lower amount of money. (There are people who drive 650 on lower priced solid state amp but everything subjective.). You can save a lot of money by going for used gears if you want to.
One cheap tube amp for 650 is Little dot mk2. You can get them used under 10k. I used them with my 6xx and changed driver tubes to better ones (subjective matter).
