Owning both the NuForce Icon Mobile and the FiiO E7, I would highly recommend the E7 over the NuForce Icon Mobile, if you can deal with the added bulkiness. The FiiO E7 has much more to offer over the NuForce Icon Mobile, such as a small digital screen with a menu, and a bass boost equalizer with four settings. (Off, 1, 2, and 3) It also has two headphone jacks for listening with a friend or whatever.
In contrast, the NuForce Icon Mobile has rolled off bass response, which made the already somewhat anemic bass of my HD280 Pro headphones noticeably even worse than using them directly from my iPhone 3.5mm jack. It does have a microphone jack, but I've never used it once. It might be useful for gaming headsets on a computer (using it as a DAC) if your sound card picks up noise from the motherboard than you can hear with your headphones when no other noise is playing.
The FiiO E7 is a little bulky, but I have it connected to my iPhone 4 with a big Otterbox case, and it is all still manageable and fits inside my pocket, though it is a rather tight fit. I attach it to my iPhone case using velcro tape, as using silicone bands blocks parts of the touch screen, and the velcro keeps the amplifier removeable as opposed to using tape or 3M command strips.
The NuForce Icon Mobile is much more portable than the E7, but sound quality is of much greater concern, especially when you're using expensive headphones.
I never use my NuForce Icon anymore since getting my FiiO E7, it just collects dust. That should tell you how much more I recommend the E7 over the Icon Mobile. I've never used an iBasso D-Zero, so no opinion there.
Also, if you need an interconnect for an iPhone or iPod, the FiiO L9 LOD works great. It has a 90 degree dock plug and a 90 degree 3.5mm plug, which is great for connecting things in a portable setup without having to deal with odd straight plugs jutting out in weird directions or getting damaged by being bent really tightly.