I would assume that the first is more correct unless HIGH and LOW were interchangeable with true and false in which case the second line would be a better way to write it.
Which is correct? or more correct? Can I always trust that second one to work?
Boolean FALSE is zero, anything else is TRUE, so you can use any value that resolves to one or the other in a boolean test. The answers from your examples depend more on how the switch is wired than the program statements used. For instance, a floating switch input is not guaranteed to be in one state or another for any length of time if the switch is open.
A boolean is simply a byte sized variable. True is non-zero. False is zero.
HIGH and LOW are defined as 1 and 0 which match the definitions of true and false.
So, either f your statements will work, under some circumstances, although I prefer the first one. It explicitly says that you want to compare the reading of the pin to HIGH.
Think about what the second statement would mean if the internal (or an external) pullup resistor is used. When pullups are used, LOW (false) mean pressed.
The reason to do this, is that you will get a compiler error if you type the wrong number of equals signs.
Personally I err on the side of extra brackets. Yes, it may look a little more crowded, but you can then be 100% certain what order things are going to happen in. Some of the order of precedences can be a little grey - if you have two operators that have the same order of precedence, which one will happen first? And can you remember the order of precedence of ALL the operators off the top of your head? Thought not. I have a good memory, and I can't - only that * and / happen before - and + (as taught in maths lessons when you're 6). So, add brackets to make it explicit. Assembly doesn't use brackets, so it shouldn't make the slightest bit of difference to the quality of the resultant code, but it might make all the difference to your calculations.
Some of the order of precedences can be a little grey
I disagree. The precedence rules are quite well defined.
And can you remember the order of precedence of ALL the operators off the top of your head?
THIS is the real problem. I can't. I can remember that the order is left to right for operators of the same precedence, that multiplication and division are higher than addition and subtraction, that multiplication and division have the same precedence, and that addition and subtraction have the same precedence.
Where ==, >=, >, <=, <, comma, dot, ->, the various shift operators, and the other bit operators fit I have no clue, without looking them up.
But, I do know that parentheses let ME control the order the way I want. So, I use them.
I think OPs use of parentheses around the comparison (as in (digitalRead(n) == HIGH)) are a good idea. It clearly indicates, to me, that it is the result of that comparison that is being assigned to the variable.