Been after a AMP, but no idea which one or if it is truly worth it.
I haven't touched either of those products, what follows is my opinion after skimming reviews. Also, the iBasso seems awesome and I will set an eBay alert for it, and buy one, if it comes up for cheap.
It depends how hard the headphones are to drive, with your combo, I'm guessing no. It seems like a pretty good setup, the iBasso head-fi reviews are overwhelmingly positive. The Audeze are well reviewed too. I have a couple low-end portable amps, I don't notice any difference with IEM's, but with my 250 ohm Sennheisers I did. A good amp is supposed to be fairly neutral so it should just make it louder and not change things too much, unless you're discussing a tube amp. This
article aligns with my limited experience in amplifiers.
One of my amps has a USB-DAC and using it makes a noticeable difference over the headphone jack in laptops. It would not have been worth it (to me) if I couldn't use it as a DAC. But your iBasso can also be used for USB-DAC functionality. Looking at the audeze specs, its only 70 ohms and the iBasso has a good dual chipset with a bespoke amplifier circuit (rather than built-into the chipset like most low-end, or mid-range portables):
The DX300 stood its ground with 4x Cirrus CS43198, and now we have the DX170 with 2x CS43131 chips. Hey, half is better than nothing, right? Both the CS43198 and the CS43131 are Cirrus Logic’s flagship DAC chips, and both share just about the same specs and features. However, the main difference between the two is that the CS43198 is a DAC only chip, while the CS43131 has the addition of a built-in amplifier. iBasso decided to implement an “exclusive OPAMP+BUF amplification after the CS43131”.
I have a set of cheap 64 ohm Samson reference headphones that I occasionally plug into a playstation controller. Some games are way too quiet so I'll use a portable headphone amp, but even the tiny wolfson DAC player I mentioned in previous posts, drives them fine.
Whether an amp is worth the money is (obviously) a personal values judgement. Back when I dabbled in it, I stuck right close to the budget end of the hobby, mostly chinesium IEM's etc, where the cost/value proposition is more pronounced. That combo is getting up towards mid-range zone and the iBasso seems like a solid device. It may not be worthwhile (for you) to invest anymore. IMO if it's loud enough once you have your EQ sorted, don't bother. If you just wanna buy gear and you live in the city, go audition some headphones with your iBasso, maybe you will find something that interests you. I've lost my will to consoom, but if I had somewhere near me that sold audiophile gear I'd like try a bunch of different enthusiast brand headphones.