The Grados don't need an amp to be driven, or to be enjoyed. But until you hear them through a strong, warm amp, you don't know what you have - or what you're missing. Grados have an open-air design, which is great for reducing HF resonance. Unfortunately, because there's no acoustic suspension, bass leaks out of them. They're not bass anemic; they're just not overwhelming the bass department. The GS1K has the best bass (even better than the PS1K, at least according to the graphs) but you won't know what your headphone is capable of until you run it through a powerful amp.
I have had an assortment of portables - including several Cmoys, several Pimetas and the Mini3. They all did nice things but nothing like my M^3 with variable bass boost. When the M^3 ran my Grados, even the most bass-shy of my Grados rumbled like the floor amp in a rowdy club. The bass was ominous, as if I were standing next to a pipe organ going down, down, down to Chinatown.
I'd had no ideas my Grados could drive so low and with so much power. To pull this off, you need an amp, and not just any amp. You need a strong amp. I used my M^3. Surely, it's not the only desktop model that could pull that off. I don't know of any portables with that kind of power. I wish I did.