First off you would need to ensure that session times/boundaries match up (e.g. not one using RTH and another using ETH), even then there may be slight (but possibly cumulative) differences between how incoming ticks are handled in two different feeds or software packages. There is some documentation in the Ninja help pages on these sort of timestamp/boundary issues at an internal level but personally I wouldn't find it troubling, it is after all down at the noise level.
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It would be normal to see slight differences in data between two different platforms or two different data feeds.
As ratfink said, the two different platforms may handle the data differently which can cause some discrepancies. Things like update intervals, how the data is time-stamped (ex. from the local PC vs the data vendor), etc can mean different outcomes. For the most part, the differences won't be all that extreme.
Another thing to consider is the data provider, in this case Rithmic is unfiltered data, so you would see some differences between a filtered feed and an unfiltered feed. Some data providers like Interactive Brokers filter their data, so if you were looking at tick data with Interactive Brokers it would be important to remember that their tick data is consolidated every few milliseconds or so. In the case of Rithmic, and other unfiltered data feeds, it is tick-by-tick and not consolidated. This means you would see discrepancies in charts if you were directly comparing a Rithmic chart and an Interactive Brokers chart. This is just an example of course to get the idea across since I'm not sure what type of feed you have running through the S5 Trader platform.
You might also slight discrepancies using the same data provider, even if unfiltered, with two different platforms as they may handle data differently causing subtle differences.
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