More light does not mean more strain. If that was the case then you could never go outside.
(Compare sunlight intensity with the monitors. You will find that it is a lot more intense).
That means your premise is false.
As to strain due to other concerns: That depends on a lot of things, most of which are not mentioned in your post. Some examples (but no all of them) are:
- Quality of both screens (You mentioned which large screen but not which laptop screen, so there is nothing to compare the larger screen with).
- Distance to the screens (to far an the 19" will be a lot easier to read. Too close and you end up turning your head a lot. Distance to the screen(s) was not mentioned.
- Height of the screens. (top of your eyes should be near the top of the screen.)