It all depends - - - mostly on what you like and maybe what you want to use it for.   The HiWall might be a bit stronger, but that wouldn't really matter since you said 45-70.   If it was me, I would buy one of each and experiment for a couple of years to see which suits your intended use best.   I like both but have 9 Sharps rifles in 40 to 54 calibers and only one HiWall, a 32-40.

I will say that for hunting in brush, the HiWall, with its centrally hung hammer might have a slight safety advantage over the side hammer Sharps.   But the Remington rolling block also has a centrally hung hammer and is as good as either the Sharps or HiWall.   Having said that, all my serious hunting has been done with my 45-70 Sharps and that has been mostly in the forest.

George

Who are the manufacturers of the replicas?   That would be the deciding factor for me.

Chris.

Premod70 wrote on Nov 19^th, 2021 at 3:59pm:

I have actually looked at a Ruger #1 and a friend has a #3 that he wants to sell.

StanR5686 wrote on Nov 19^th, 2021 at 4:29pm:

Be sure to shoot the two versions before investing in one. Most folks will pick the #1, the #3 is a recoiling beast in 45-70.

While I am not familiar with the Uberti High wall I do have a browning, a rolling block and a sharps. The rolling block is italina in origin, the sharps is a Shiloh and the browning is custom. The highwall probably has the fastest lock time. the roller the slowest, the Sharps in the middle. But truthfully all 3 are faster than you might think. The drawbacks on the Browning and the roller is they just extract. The roller if you run it smartly will or come close to ejecting the fired case. The sharps will easily eject a fired case even with a tang sight in place. As to the accuracy that all depends on the barrel and not so much the action. All can and will shoot well, as well as all can have a bad tube on them. Am not sure if any of the 3 Italian rifles come in what you would call a hunting configuration. The target models are heavy if you are going to be doing much walking. Of my 3 the roller is the lightest at 10 1/2 pounds, the other 2 are up in the 12 pound range. I think Shiloh makes a saddle rifle that would be easier to carry around, maybe take a look and see what Bill Goodman has on hand or has coming in. 
Sam

I prefer the 1885's center hung hammer for it's faster lock time, and the 1885's firing pin for more consistent strikes, and less chance of breaking a firing pin.
I have no experience with Uberti rifles, but Pedersolis are very accurate. I'd probably be more inclined to go with either the 1885, or the Pedersoli Rolling Block myself.

I quit keeping track of my 45-70 reloads about 20 years ago, (or more) when I hit 10,000. Most were fired from a Sharps and the rest with a trapdoor. In 2007 I bought a Highwall and have done very little shooting with the Sharps since then. I still like it and its a great shooter, but I had to replace several extractors and firing pins. If you read the reports from the 1800s, the two main complaints were firing pins and extractors. Another factor to consider is whether or not your Sharps has a gas block at the rear of the breechblock. If not, retro-fitting one is a MUST! I learned that lesson the hard way- a pierced primer and lots of hot gas and tiny particles of brass and powder in my face. 
I have done most of my shooting lately with the Hi Wall (Uberti) and never had a problem. Its a simpler and much better design, especially the firing pin. 
If you like the lore of the buffalo rifle and want a Sharps, by all means go for it, its a great rifle.  Shot several deer with mine and won lots of Schuetzenfest medals with it. If you really want the BEST rifle, its the High wall. 
Another option which many people unfortunately overlook is an original trapdoor. Very accurate, easy to sporterize, lots of interchangeable parts, ( I  have NEVER  had to replace a part). I would not butcher a nice rifle but there are lots of cut down rifles that can be dressed up.  The only disadvantage is you really can't put a scope on it. But a quality tang sight is an option. 
My Sharps was made by Palmetto, very satisfied with it. The High wall is a Uberti, won a lot of medals with it (way better Schuetzen target rifle than the sharps) .
The trapdoors are all originals, would not mess with a replica, no need to, good  original shooters  are plentiful, reasonably priced and great quality. I dont think the parts on replica Trapdoors interchange with originals. 

I hope this helps!
Joe S