I haven't used the U3 myself. Right now I'm using a DSS, analogue out to my tube amp, and I'm not particularly interested in seeking another DH product. I sold my Recon3D USB in a bundle with my AD700 headphones, a "complete gamer kit," but I miss the Recon, and I had it plugged into my computer via USB (dual-boots Mac and Windows, and it continues to provide power through USB even if turned off) and optical to my Xbox at the same time, then a headphone-to-RCA cable into my tube amp, then Q701. I don't currently own a proper external DAC, unless you count the DSS (works in stereo with the PC, but I don't use it that way), but that'll be the last thing I'll upgrade.
I'll actually make a weird recommendation. First, just plug your K701s into your device. It ought to still impress you with better refinement and detail, and be a clear upgrade. Then, save up for a good amp later, one you won't need to replace. It'll be like two surprises in just how great things can get, and you'll end up with a better amp.
I use a custom-made tube amp (a super simple 6DJ8 amp), a FiiO E12, and in my old apartment I used to use my Yamaha receiver for simplicity's sake (DAC, amp, surround processor, input switcher, and speaker amp all in one, with a remote control for bonus). Oh, I also used a FiiO E5 at first, that was ok and it did take a bit of the edge off of the treble, but better amps were better. Other good recommendations for amps are around, but I feel that tonally they're all pretty close if they're solid-state amps (which is partly why I'm playing with tubes), so pick one with a good match in high power and low output impedance.
I personally think THX TruStudio Pro was also an advantage of the Recon3D USB, but that's a taste thing.