A few personal opinions:
1) The difference between the HD650 and HD600 is fairly pronounced. The degree of tonal difference is fairly small, but the overall effect is that the HD600 is neutral to a fault while the HD650 has a warm, creamy coloration with recessed (but not rolled-off) highs and boosted bass.
2) I can't see how the HD650 would be considered harsh, and I don't think the upper mids/lower treble are boosted at all. However, I can see how the HD650 can be considered fatiguing in the long term. It needs volume in order to shine, and at that volume, the combination of big slam and slow transients starts to grate on my ears, after some time.
3) In terms of transient response/speed and resolution the HD650 is superior to the HD600; it also reaches further down in the bass. If only it had a neutral tonal balance! Sennheiser specifically voiced the HD650 to have a tonal balance that's more appealing to high-end consumers... except that the selfsame high-end consumers usually voice their own systems however they want, or are professionals that don't want a pre-tuned headphone.
Or, I could be wrong. My recording engineer friend uses HD650's, because they approximate the tonal balance of a consumer system while possessing high resolution. Still, his neutral reference headphone is the HD600.
4) The HD600 is, in my opinion, one of the best dynamic headphones ever made. It does things that no other dynamic headphone can - to my ears it's neutral to a fault (I think that the word "neutral" has become synonymous with "bright" in a lot of hi-fi publications and communities, but this headphone is well and truly neutral), has a very accurate tone and tembre, and portrays instruments very realistically. It does struggle with texture, and it is, well, one of the slowest hi-fi headphones out there, if not the slowest, so its abilities with complex music are very limited.
5) If the HD650 isn't doing it for you, while the HD600 is, then get rid of it!. Don't let anybody persuade you otherwise. Sure, you can drive the HD650 balanced, from bright, aggressive sources and fast, lean amplification to make it less dark and laid-back, but as a general rule, system components will fine-tune a speaker's - and a headphone's - performance, but they will not radically alter it. You need to start with a speaker or a headphone that you like, and then build a system around it. If you're fortunate to have a headphone that neatly fits into your sonic preferences, then use it and be done with it. There may be other headphones out there that you'll like (just you wait till you hear the HE90), but that doesn't mean that you have to throw away what you already like to get them.