The Spencer was by far the better of the 2 weapons. A weapon has no greater accuracy for the most part than the person's ability to shoot the weapon. The Spencer fired a bullet around 350 grains with a powder charge of around 40 grains, this would depend upon the manufacturer of the cartridge as there were many different loadings for the Spencer round but most were close to the above loading. This gave a muzzle velocity of around 1200 fps with a muzzle energy of around 1250, again plus or minus a little.
The Sharps had the bad habit of fouling the action after a few rounds which would greatly cause functioning problems but also accuracy problems after the barrel was fouled out. While the action for the Spencer usually did not foul, the barrel would and there goes the accuracy. Fouling is the "destroyer" of accuracy. NRA BPCR shooters use a blow-tube between shot to keep the fouling soft. The Sharps fired a bullet around 425 to 450 grains with around 50 grains of black powder, again this is depending up on the loading by the manufacturer or arsenal. The velocity is about the same as the Spencer as is muzzle energy.
While a person could fire a Spencer at a rate of maybe 14 shots per minute, the Sharps was more in the 5 shots per minute range. I own and fire both the 1859 Sharps double set trigger model rifle Pedersoli and the Spencer rifle, both original and Armi Sport. The rate of fire of both is not what many may feel it might be.
As to the power of each rifle, they are very comparable. Contrary to the movies and what some may think a Sharps will not take off whatever body part it hits, especially at 200 yards. All black powder cartridges have a giant rainbow trajectory at long distance. The .45-70 has about a 25 foot midrange trajectory when shooting at 500 yards making hitting at unknown distances almost impossible with first shots. The Spencer round as well as the Civil War Sharps round would be greater in their trajectory. The reason for good target shooting accuracy with bp cartridges is that the shooter are firing at targets of known ranges and can adjust their sights according. The Civil War soldiers were mostly shooting at unknown ranges and a misjudging of range, of a few yards, means a missed target. On the other hand "Minute of Buffalo" is far easier to achieve.
As a Union soldier there is not doubt which rifle to choose, the Spencer. Ammunition supply was not a problem, at least for the Union. The Spencer rifle was not a common weapon since only about 11,000 were made. This is about the same as the number of Henry rifles used in the Civil War. The Spencer carbine was much more in use, mainly by cavalrymen, since about 65,000 were issued by the end of the Civil War. The Spencer is my choice if I cannot find a Henry rifle. The Henry Is a better weapon in my view as a Civil War soldier's weapon.