JMX--
I've used both the Steel Heart and the Randall #1, as well as other Busses (various) and Randalls (Fireman's knife and Mod. 25 hunter).
Three observations, and these are just my own predilections and reactions, based on my experience. No criticism of Randall's per se, as they have certainly proven themselves in the field for generations.
1.) Handle design. The Randall handles are round and comfortable--until they get wet. Then you lose the ability to torque the blade by applying grip alone, because the wet round handle turns in your hand like a bearing. The shape of the micarta handles with finger indents mitigates against this problem, but the smooth micarta they use is also slicker than the standard round leather handle. Personally, although the Randall handles are actually more comfortable to hold than the Busse "E" models, for my hands, the Busse's offer a much more secure grip. The Busse handle is flat, for power in torquing. It is also textured, for a non-slip grip. And its contours keep the handle in the hand during vigorous activity such as chopping or stabbing/chipping. The Busses are also more comfortable over a wider range of holds than the Randall grips with finger grooves, just because when you turn the handle upside down for a pull cut, you don't have finger grooves digging into your palm.
2.) Tang construction. Here again, Randall has a reputation for durability that I'm not qualified to question. However, the full tang of a Busse to me seems an obviously stronger design than the stick tang of a Randall.
3.) Steel. INFI vs either (a) Sandvik stainless or (b) the simple carbon steel used by Randall--don't recall what it is. I think that choice speaks for itself.
Although I've not tested the knives side-by-side, my impression from my memory of using Randalls is that the Busse's slicing ability is also superior, especially on harder material like rope, which is probably a result of Busse's full flat grind. I sold all my Randalls for the reasons given above, long before I bought my first Busse. I currently have 8 Busse's plus one on order.
-w