Green frog: I agree 'bout the M 1885 High Wall, & I'll add the M1878 Sharps-Borchardt.

I once knew an Old Time Shooter who claimed that the best aspect about the Remington Pattern Rolling Block was the "ear" on the block. He claimed that w/ a judicious application of a boot heel, the Shooter could aeat a problemmatic cartridge!

I must say, up front, that I am not a particular enthusiast for any particular single shot action. Different actions are "more" suitable for certain uses than others.

For instance, I am a serious fan of .22 rimfires. The high wall Winchester, while an extremely well designed and especially well machined action is NOT one of my favorite for a .22 rimfire. It is awkward to load and manage the small .22 rimfire cartridge with a high wall. I like the low-wall better for the .22 rimfire cartridge, but it is still not one of my favorites (unless it has the original beveled top breechblock). There is a reason for my preferences regarding the rimfire:

The .22 rimfire uses fixed ammunition with lead bullets (everyone knows that, of course). It is VERY advantageous to have a .22 rimfire with a match chamber. My favorite type of match chamber (they come in various flavors) is a Clymer. It engraves the bullet of the fixed .22 rimfire almost to the case mouth ensuring proper bullet alignment with the bore - this has a very positive effect on accuracy. The problem comes in in seating a rimfire in this tight, match, chamber. A straight falling block action does not do this well. Your thumb will last thru about two seatings of a cartridge before it becomes too sore to continue (been there, done that). The original low-wall chambered for the .22 rimfire had/has a bevel top edge to the breech block which will work with this particular type chamber. 

One of my favorite actions for the .22 rimfire is the lowly 44 Stevens. The Stevens has a "rocking block" action that very nicely seats the fixed ammunition in a match chamber. I have an original 44 Stevens that I had re-barrelled with a Shilen match barrel with Clymer match chamber. It handles extremely well and shoots with match authority. The 44½ Stevens also has this property. Both of them lower the breech block out of the way of the barrel end making it easy to "find" the chamber to insert the tiny .22. The Ballard has long been a favorite of the .22 shooters because of it's seating action and ready access to the chamber. It is also one of my favorites.

Probably the absolute best value in a totally favorable action for .22 rimfire use (serious target work) is the BSA Int'l series. That is my personal choice for serious bench work. 

There are other considerations, of course. Trigger availability is one of those. The CPA Stevens 44½ is available with double set triggers. The Ballard, as made in Cody, Wyoming, as well as originals, is available with double set triggers. The low-wall Winchester is available with dbl set triggers. The BSA's are no longer made but there are still a good number of them available. They are not available with dbl set triggers, but the latest issues (Mk III, IV, and V) can be adjusted quite light (around 8 ounces) for a really quality, trigger pull with extremely fast lock time.

Center fire is another ball game entirely.

Dale53

As has been stated before, the answer to your question depends on what you want to do .  If you want to use it for rimfire competition, the BSA MKII falling block is as good as any and better than most. For target work, the RB and Sharps are usually chambered in cartidges that are larger than the traditional Schuetzen cartirdges but are fine for the old traditional black powder cartridges.  The Sharps is probably the least reliable.   The trapdoor does not have a metal tang for mounting a tang sight, but if you build one up from parts you can have one put on. In that caase the Trapdoor can be very competitive with the sharps and rolliing block, with a good barrel and trigger job. I have fired well over 20,000 45-70s in several Sharps and Trapdoors, and never had to replace a part on a trapdoor, cant say that for the Sharps. Loading and unloading the trapdoor is very fast. The three position tumbler on the trapdoor is a nice safey feature for hunting.  The trapdoor is plenty strong enough for smokeless loads in the old blackpowder velocities. Did I say I was a trapdoor fan?  So if you want it for centerfire comepetition or hunting , trapdoor is a viable option. I like them all, but the trapdoor is certainly one of the most reliable and well made. Joe S

Falling block. Designed later and better.