First of all, are you going for extreme accuracy with a tricked out 10/22?
If not, one should consider the capabilities of a 22 LR cartridge- If you were to get
1 inch groups at 100 yards I would think you have an exceptional rifle/ ammo combination.
IMO 3/4 inch at 50 yards would be more realistic and "operator error" has to be considered especially if shooting positions and not bench rest.
A rimfire 22 lr scope has a fixed parallax set at 50 yards and IMO a very excellent, high priced scope is not really needed. Your Burris on a 223 probably has a parallax at 100 yards plus which is too far for a LR.
I have a fixed 4 power 30 mm objective Simmons scope and find it more than adequate as it brings a 50 yard view down to 12 feet and has a large enough field of view so I can find targets quickly and in low light. Many like a 4-9 power scope, especially if hunting squirrels, chipmunks etc.
You do not state what kind of shooting you will be doing as this really makes a difference in your choice.
Check your Burris scope info for parallax and just in case it has a 50 yard parallax.
If so mount it on your 10/22 and get another scope on the 14.
Just some thought to consider