I'm a newbie here and please help.
I'm just about to create some content for one of our partner sites, which promotes our brand and product without linking to us. Is it best to use the same keywords as our main site, or use another relevant keyword(s)?
It's probably best to use a combination of both. By using the same words, you reinforce the message of what the page is about. But by using different words, you suggest an independence between the sites, and you help to mop up people who search for different words to the ones you have chosen.
If your promoting a particular product or particular category only then you can use specific keywords related to that product and link it your site also so that you get visits from your partner site for other products as well.
I agree with Stevie that it's probably best to use a combination. But I wouldn't get too obsessed with it. The important thing is to write persuasive promotional material. Focus on that, rather than worrying about what keywords the copy contains.
Use different keywords and never use the same one again and again, Google treat repetetive keywords in anchor text as a spam and the result is not good, so use synonyms and even long tail keywords to be natural and better.