I have a TD and 3 other 10/22s. One of them is a build with a 20" .920 barrel and a Fajen target stock .... a real tack driver. When I shoot my factory TD, side-by-side with my factory carbine or factory stainless Mannlicher , using factory iron sights, there is no difference in accuracy, even if I take the TD down and put it back together. That's because the iron sights are mounted directly on the barrel. Where there is a notable difference is when I mount a scope on the TD. Because the scope is on the receiver, any small change in the barrel-to-receiver fit will affect the TD's accuracy ... worst case, maybe a 2" difference in POI at 50 yards, but usually less than 1" @ 50 yards. BTW, unless you do some custom work, such as a match grade barrel, 10/22 are not particularly accurate. All my 10/22s will shoot under 2" groups at 50 yards on a good day. My build will shoot sub inch groups at 100 yards on a calm day... big difference. I have a CZ bolt action 22 that is a tack driver, right out of the box. Point being, if you want precision accuracy, you might want to consider a bolt action. If you want a really fun plinker, get a 10/22 in either platform.
My vision doesn't agree with a red dot because it looks like a red cotton ball. Scopes seem to work well for me; however, I shake quite a bit so 4X is the max magnification for off hand shooting with my 10/22. For bench rest shooting, I can do pretty well up to 10X.
Here's my TD with a 4X32mm Ruger scope. It's a cheap scope but it serves my needs. I can easily hit soda cans at 50 yards.