3 ms·
I would do both: product.company.com and (www.)company.com/product/.
I would do both: product.company.com and (www.)company.com/product/.
That splits your link juice to no positive effect.
Having one redirect to the other is a decent idea. That's what google does.
http://analytics.google.com http://analytics.google.com
http://google.com/analytics http://google.com/analytics