I am an intraday trader and Day’s open is crucial for me like any other intraday trader. When market watch and intraday chart displays two different day’s Open prices which one can a trader choose as a better reference?
Firstly (copying from my earlier answer)
Tick Data: Market data that shows price and volume at every print, it also includes information about every change to the best bid and ask.
In a single trading day, there are millions of such ticks recorded (remember this also includes change in best bid and ask prices) and it is technically not possible for any trading platform to show all ticks, especially live and on a normal broadband internet connection.
If you really want to see all the ticks, NSE does have Tick by Tick data feed which is a lot more expensive than the normal data feed, and will have to be subscribed to througn any of the authorized NSE data vendors (Not all of them give you tick by tick data). Also to be able to make best use of this tick by tick data, you should ideally be on the NSE collocation which would mean that your systems are inside NSE itself, so that accepting all the millions of ticks will be quite efficient.
Tick by Tick data is usually what professional High Frequency and Arbitrage trading firms use, don't think there is anything much a normal retail trader can do with it.
Now, when the market opens first thing in the morning, there are lakhs of orders fired in the first few seconds. Some of them market, some limits away from the current price. So usually there is a lot of chaos. Firstly as explained above, no trading platform will be able to capture all the ticks (upto 8 ticks per second at the max, whereas there could be thousands in reality). To know the true open price, you will either need TBT data from exchange, or wait for bhavcopy from the exchange in the evening when they tell you the exact open, high, low, close price for the day.
Personally I think, nothing much should be made of the open price that you see on the chart or marketwatch. Firstly they very easily couldn't have caught the exact open, but even if they did, it may not truly indicate the actual opening price because of all the chaos in the first few seconds.
I'd say, true open price is when the initial chaos ends. So i'd say close of the first 1 min candle is a best indication of the true open price for the day.
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Thanks Nitin !
Makes sense 
Keep up the great job !