I think the following would make better sense and mean the same.
Children read books less often today (these days) than they did before (in the past).
Children don’t read books as often today as they did before.
If these are intended to convey the same meaning as the sentences in you other thread ‘people or the people’ then both sentences are incorrect. Here you are comparing the SAME children (which doesn’t make much sense at all), not two different sets of children. ‘They’ has to refer to ‘children’ here and your use of ‘before’ just indicates the same children when they were younger.
You need something like:
Today’s children read books less often than children have in previous generations.
Today’s children don’t read books as often as children did in the past.
Then they mean the same. I don’t think either are particularly “common” or “uncommon” but I have given a streamlined version from the PoV of a native English speaker* in the other thread. If you want the most common sentence, it would probably just be:
Children now don’t read as many books as children in the past.
*Note I don’t just use the term ‘native’ in isolation as that is non-specific, so would be unhelpful and incorrect.