By "blurry", I'm going to assume you mean it got stuck at a lower resolution.
It may be a driver bug, where it forgets that HDMI 1.3 supports the native resolution of those monitors. Or it might be some kind of hardware limitation, where HDMI 1.3 is only supported if the DVI-D isn't used. I just don't know the details well enough to guess.
But I can tell you how to get the two monitors working perfectly, though not precisely, because you did not indicate exactly what graphics card you have (there are many 7870 models available, with different connector options).
The short answer is, use only DisplayPort or Dual-Link DVI-D to connect the monitors.
The longer answer depends on what connectors you have available. In general, the card will have either one normal DisplayPort connector, or two mini-DisplayPort connectors. They are electrically compatible, so a simple passive adapter will convert between the two. The card will also have one or two DVI connectors, though only one of them will be Dual-Link.
If your card has only one DisplayPort connector, then you will have to use DVI as well. If the card has two DVI ports, you must determine which one is Dual-Link. In every case I've found, this will also be the one port that also supports analog VGA. If the same connector part is used on each, look for "VGA" next to one. If the connectors are different, look for the one that matches Dual-Link DVI-I here. Make sure you have a Dual-Link DVI cable. There should be no gap in the middle of the pins, as you see in the Single-Link picture at the Wikipedia link. Dual-Link DVI-D is fine, since you won't be using the analog pins.
If you have two mini-DisplayPort connectors, you can run both monitors that way. Use either DisplayPort to mini-DisplayPort cables, or normal DisplayPort cables with adapters to reduce the connector on one end to mini-DisplayPort. If just the one connector, use a normal DisplayPort cable.
As to which monitor you plug in where, it doesn't matter. One will be labelled #1, and one #2, but they can be arranged however you like.