1. Tonality (mid-tones, highlights)
2. Separation
3. Grain
4. Speed (shadow detail)
Rodinal and HC-110 are my two developers, w/ Tri-x, a combo used for 98% of my work. I keep both on the shelf, b/c they're both incredibly flexible (Rodinal more so), but they're also extremely different from on another. Also, I use both 1+50.
1) Rodinal is all about the mid-tones. HC-110 is the opposite of this, all about the highs and the lows...but mainly the highs.
2) As above Rodinal has separation in the midtones, but uninspiring highlights. HC-110 has highlight seperation unlike any other developer I've used, sparkly.
3) Rodinal is incredibly sharp, and once you get used to it everything else looks funny/soft afterward. Grain is there, but grain is controllable, and can be sharp and gorgeous once you learn the developer. I actually can get the grain pretty darn tight in Rodinal with the right mix of agitation and dilution. HC-110 isn't a low grain developer by any means imo. but less so than Rodinal, and moreover, simply, different. HC-110 can also build edge effects and accutance, but I don't think the sharpness there is as pretty as w/ rodinal...it has something to do w/ how it mixes with the other characteristics of the developer.
4)Say at box speed, on the neg, I actually get more shadow detail with Rodinal than with HC-110. But this seems to go against what other say, and I don't have a densomiter or anything, so I'm likely not correct by the #s here. I do think HC-110 looks better at 800 and above. Rodinal can be interesting, but it get's a chalky graphic feel when I've pushed it. HC-110 really holds up and has less base fog.
I really love both. I think Rodinal took me longer to learn what I wanted to do with b/c it's so transformable and is a developer that can be pushed to extremes w/ great effects.
HC-110 has much much shorter dev times for my regimen, which is good thing if controlled, keeps the wet time to a minimum. This can make a subtle difference, but I believe it's there.
In general, I look at it this way: HC-110 gives me a really great neg that I can pretty much take straight to print. Just looking at the negs, the shadows are already deep and the highlight already bright. Clean and easy, but it also takes on a delicate nature b/c of this (hard to put in words) and doesn't (for my work) hold up to any heavy handedness in the print. Rodinal is the very opposite. It gives me a really meaty neg that I almost never print straight, but there's so much there tonally that I can push the neg extremely far in the print, be heavy handed, and the further I go the better it looks.
I wrote this all up quickly, but hopefully it helps!