I believe that the general consensus--based on many range reports--regarding .22LR vs. .17HMR accuracy is that the .22 is slightly better. But there are a number of layers to this. First, with the .22, true match ammo is available, whereas with the .17, no such quality level exists. So, when comparing accuracy, it's important to specify which .22LR ammo is being used. If we're comparing Eley Tenex, Lapua Midas+ or RWS R50 in .22LR with just about any of the available .17HMR loads, and we're also talking about rifles of similar quality--like an Anschutz 1712 or 1710 in .22LR and an Anschutz 1717 in .17HMR, or similar-quality rifles in each cartridge from Savage or Marlin--then the .22LR will come out ahead at 50 yards. I don't think there's much disagreement about that, based on the many range reports I've read, along with my own experiences with the two rounds. On the other hand, things might be much closer at 100 yards, where the .17's wind-bucking ability is superior to that of the .22LR, although the difference is far less than many think--about 1.0" more deflection for the .22LR sub-sonic load than for the .17HMR load in a 10 mph cross-wind. Interestingly, the high-velocity .22LR load deflects more under these conditions than does the sub-sonic load. So, at 100 yards, the .17HMR might shoot as tight groups as a .22LR with match ammo.
However, if we're restricting our comparison here to 50-yard group sizes, a good .22LR with match ammo will generally shoot slightly tighter groups than a good .17HMR with the available .17HMR ammunition. What a lot of us would like to see is one of the ammo makers offering match-quality .17HMR ammunition, but there's no sign that this will happen any time soon.