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I'm trying to understand which of the following limit orders would be filled first.

Let's say for argument's sake stock X is $11.00, person A makes a limit buy for 1 stock X at $10.00 at 10:00am market open and it hasn't been matched. At 3:30pm person B makes a limit buy for 1 stock X at $10.00 and its not matched. At 3:31pm the market price of stock X hits $10.00. And someone makes a market sell of 1 stock X.

Whose order is filled first? Person A or Person B? Would the filling criteria differ from exchange to exchange or do all exchange operate on the same matching rules.

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    What do you mean 'the market price hits 10$'? There is no 'man' that names the market price, that's unfortunately a common misconception. – Aganju Feb 4 at 6:48
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By placing a market sell order it will take out the highest buy order in the order book. So, in your scenario, the market sell order at 3:31 pm would take out A's order to buy at $10.00 if it is the highest buy order remaining in the order book. As orders hit the order book at the same price they will go behind all the other orders already entered at that particular price.

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