It's never really clear what the "full package" is, but Sky Sports only comes in SD as standard unless you have a separate HD add-on for them. Some packages include the HD supplement as part of it, but it still remains an add-on.
Given you have a TV360, you'll be selecting Sky Sports on Ch501-510 regardless, but it may make a difference as to whether you're accessing SD or HD versions of those channels - that's where I'm going with this question.
Swapping your 2 TV boxes around can't do any harm, but may just help prove that the issue is box-related.
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