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From what I understand, the higher the Treadwear rating, the longer the tire will last, so therefore it should be the hardest rubber compound and lowest rolling resistance?
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This is not necessarily true, as I have heard that different companies have different ways to rate tread wear. Couldn't hurt to pick the highest one though. Also, there is more that factors into rolling resistance than just tread wear rating, however that is one factor.
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Would the tire with the lower Traction rating also be the better choice for LLR, as worse traction would mean lower resistance?
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Again, not necessarily. You can be sure, though, that the tire with the lowest traction rating is less safe than the tire with higher traction rating. And again, less traction doesn't always mean less rolling resistance.
All in all, if neither of the tires are advertised as being a "low-rolling-resistance tire," then just go for whichever one you think would be the safest or last the longest. As a side note, you'd probably get better gas mileage with a tire rated at a high max sidewall air pressure (psi). So, if one is 44 and the other is 36, I would pick the 44.
Hope this helps,
JMac