A major appeal of a bus-powered USB interface, just like that of a laptop computer, is mobility and portability, since it can allow recording and mixing to be performed away from a source of mains power.
But the basic reality is that the power available from each USB2 port on a computer is limited, and may be especially so in the case of using a laptop computer running on battery power where battery life is of primary concern.
(Btw, this limitation affects not only USB bus-powered interfaces but has also affected the usability of Firewire bus-powered interfaces with laptop Cardbus/Expresscard FW cards which require connecting a power cable to a USB port on the laptop for supplying bus-power, which accounts for why many Cardbus/Expresscard interfaces include or even require a mains adapter.)
Now, an obvious way of coping with the power supply limitation of USB ports is to simply limit the features and capabilities of a USB bus-powered interface so as not to exceed the available supply power, as I'd already mentioned, and this has pretty much been the norm especially at the lower cost end.
Fortunately, as the USB audio specification has evolved and lower power components have become available (and at lower cost), manufacturers have been able to offer more capabilities in their bus-powered USB2 interfaces including, more recently, more I/O and an onboard DSP mixer/fx, features previously only available on mains-powered units. But even so, the mic/inst preamp gain/headroom and headphone/line output power of bus-powered interfaces may still be limited compared to mains-powered offerings.
Bearing this in mind, when auditioning a bus-powered interface, be aware that the power output of its headphone output will very likely be rather limited and that it is therefore essential that headphones of the proper impedance (referring to the interface's specifications) should be employed. But even so, the headphone output level of a bus-powered interface may seem low/weak when compared to a mains-powered interface (because it very likely is, although on the upside it's not as likely to pose a hearing loss risk).
Btw, another way of coping with the power supply limitation of USB ports is to draw power from an additional USB port(s), which is precisely what RME do, supplying their USB bus-powered Babyface interface with a special USB cable having a second USB connector for taking power from an additional USB port.
Another reality is that connected USB peripheral devices must negotiate for the amount of current to be supplied over the USB interface, during device enumeration (configuration), as well as abide with system power management regimes. This has complicated the design and slowed the availability of more capable bus-powered interfaces with onboard DSP/microcontrollers even from larger companies like Roland and Yamaha which can develop and produce their own dedicated logic and signal processing chips for their interfaces unlike the smaller manufacturers which must typically buy-in such components and solutions. Which probably goes a long way towards explaining why we are still seeing new USB2 interfaces being launched these days when USB3 ports abound on every new computer.
Returning again to the question raised in the OP, as to whether any bus-powered units will have issues, consider that the Roland Quad-Capture can provide a maximum phantom power current of 6mA at 48V.
Then consider that the vast majority of phantom-powered condenser microphones on the market were designed for connection to mains-powered mixing consoles, not to the mic inputs of bus-powered audio interfaces, and that besides requiring a small amount of phantom power for polarizing their diaphragm capsule some mic's may also have onboard drive electronics which also must draw phantom power (the Rode NT2a comes to mind).
Once one considers these factors, it becomes easier to understand why people might become frustrated when unable to use more than a single condenser mic at a time with their bus-powered interface (the NI KA6 comes to mind).
If you don't understand what the specifications mean, then learn (try a glossary). Besides possibly saving you from making a bad purchase decision, you're more than likely going to need to know some of that stuff anyway if you ever hope to get serious work done in your studio.
Some bus-powered study material:
http://tascam.com/product/us-366/specifications/ http://www.native-instruments.com/en/products/komplete/audio-interfaces/komplete-audio-6/specifications/ Note that sometimes it's a spec which you won't find listed which may be important (and may raise a question as to why it's not been given).
Ok, enough on this.
Good luck with your purchase (especially if you try to B-S your way through it)!