Pianist, the HC1000 aren't really isolating. Those are tiny closed-back headphones with small enclosures. They isolate a bit better than maybe Sennheiser PX200, but it's far from the isolation Denon AH-D1000 or AKG K-26 (K-27, K-414, K-416 JBL 410, etc.) have. About the same isolation as earbuds (maybe a bit less).
They are very sensitive though, and driven by an amp like Minibox-D there's going to be enough frequency bandwidth to filter out ambient noise; they were pretty good at filtering out underground noise when playing. Out of the Minibox-D, they're even "sweeter" than the AH-D1000 (the Minibox-D makes AH-D1000 show its slight muffledness and backwave echoes).
The HC1000 are a much better choice than any earphones, none of the comfort issues, and they take up about the same space when folded (fit into a shirt pocket just like a pouch with canalphones or earbuds would). Sensitivity is the same as most earbuds (113 dB/mW).
In short, the HC1000 are almost like earbuds turned headphones - very easy to drive, excellent space/dimension of sound/treble extension even without an amp, very good clarity/detail, but they have a minor dip in the lower midrange and they're not as bassy as, say, Porta-Pro. The low register is all there, unlike PX200, but there's not much bass bloom or sub-bass bloom (for those into that) - a more polite definition of bass. Not basshead headphones, though for a classical music or jazz listeners they're just the thing (acoustic bass, percussion and low strings won't ever overpower other instruments).
