The difference is how high your scope will sit off the rail.
Things to consider: Sights - Do you have iron sights you need to be able to see over? If you do and want to still be able to use them you can get what are called "see through" scope mounts. Eye relief - How far back do you have to have your face to see through the scope clearly. Face - How high does your face naturally fit on the stock? do you have to move up/down to see clearly? This would mean you need different height mounts.
Scope mounts will have nothing to do with your accuracy. Accuracy will depend soley on the weapon and your ability as a shooter.
However, if your problem is that you are not able to adjust your scope onto paper, then yes, different mounts might fix your problem. There are different styles that will mount better and different height mounts may help you get your scope in line with your rifle.
Here are a few examples:
These are "see through" mounts.
Mounts like this are typically pretty solid. Notice the minimal parts and the "central" adjustment screws on the top to tighten the scope into place. This way you won't rotate the scope as you tighten it, helps keep your cross-hairs level.
These are garbage IMO... thats why they are on my CQB set up with a massive red dot where accuracy doesn't matter and not on my RS. Notice the one screw on each side and the 3 part mounts to get it onto the rail. With these you will have left - right variance between the mounts, thus throwing your scope off of alignment.
Typically these are the kind of mounts I try to go for. Notice the multiple screws on each side of the ring and notice the one sided clamp to the RIS rail. This helps keep your scope in line both in the rings and on the rail.
Here is a pic of various height rings... this will differ between manufacturers.
TLR - More screws holding the scope on the rings + less screws holding rings to the rail = Good.