A better amp isn’t about being louder... it’s about being clearer and cleaner! The HD 650 has more resistance than most headphones... and with a weaker amp, sometimes you can hear the headphone resisting the note changes.
There are many nice amps on this site perfect for the HD 6XX/650... I personally love my Cavalli Liquid Carbon (the original before the Massdrop “X” version), and I’ve liked all of Cavalli’s gear I’ve heard at CanJam and other trade shows, but I’ve also enjoyed the iFi gear so I’m curious about the brand new iFi ZEN CAN Signature products specifically designed for the HD 6XX. The Darkvoice and La Figaro were two examples of tube amps that I believe were both sold here on Drop: it’s hard to say exactly how they sound because each tube can drastically change the amp’s sound, but that’s part of the charm. The downside of tube amps is that sometimes you’ll pick up noise, squeals, or buzzes/ringing from other electronics like cellphones, or bumping the table. Tubes do eventually burn out and need replacing, but they can last a really long time... certainly longer than my light bulbs! I have Sennheiser’s HDV 820, so I don’t need anything else, but I’m still a curious person 😁
I used to own an Audio Technica ATH-AD700. To describe it, the emphasis was on the upper mids and treble, so female vocals and violins will especially stand out forward in the mix (as forward as something with a lot of soundstage can be), but there was a noticeable de-emphasis on foundation instruments and bass instruments, leading to quite a lean sound. A brief demo of the AD900 had a bit more lower mids, but I still experienced a pretty lean sound.
The HE-4XX will have a tuning similar to your Denon D2000, with a bit of bass and treble emphasis (but not as much as the Denon, and the HiFiman will sound more open and separated because... it’s an open headphone), and it’s always interesting to have samples of different driver tech (HE-4XX is a planar magnetic, Denon D2000 has a dynamic driver made of bio-cellulose, HD 6XX has a dynamic driver made of a proprietary plastic membrane with silk acoustic dampening). Check HE-4XX reviews (or their discussion thread) for more descriptions and impressions.
However, the HD 6XX is more vocals emphasized and should provide an interesting contrast to compliment what you already have. The highs just beyond the range of female vocals are just a tad relaxed to reduce fatigue for long-term listening, but it still has a “natural” tone. The combination of 300 Ω resistance mentioned before and the treble “recession” are the parts that some people refer to as “veiled” or “warm,” but the HD 6XX is highly capable of presenting detail and an extended treble response beyond the pitch range of human hearing. With a proper amp, you may wonder why people have said “veiled,” because where’s the muffled/occluded sound? Vocals are forward, but overall it has a balanced and full sound.