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1. That's a movie I won't be seeing/watching again.

2. That's a movie I won't see/watch again.

What's the difference in meaning between the above sentences?
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I don't see any difference in this context. When used in terms of sight, see and watch can be used the same way. "View" can also be used, though I hear it less frequently. "That's a movie I won't be viewing again."
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My question is:

What's the difference between the future progressive tense and the future tense in these sentences?
I will use " the " definite article.

1. That's a movie I won't be seeing/watching again

In the particular time in the future, the action of seeing/watching will not occur and it will not in progress when something or someone happens.

2. That's a movie I won't see/watch again.

At one particular time in the future, this will not happen.