We prefer to think of him as "curmudgeonly."
The question I have is this (and it is actually related to what Chris was asking): why do you want to set up a second site, as opposed to adding these products and this content to your existing site?
See, as he said, it's a business decision, not an SEO decision.
If you're doing this because the two sites would be targeting totally different audiences, or if it's because the products are totally unrelated (machine tools & Italian leather men's loafers, or gourmet kitchen gadgets & industrial solvents, for instance), then it might make business sense to have two separate sites. On the other hand, Amazon, Ebay and others seem to have made the "little bit of everything" concept work for them, so it's possible with some solid planning, well-thought-out site architecture and good internal navigation you could make it work on a single site.
If, on the other hand, the sites would be serving similar audiences and/or selling similar or related products, then you're almost certainly better off adding them to your existing site. It's generally less work to promote and maintain one site than two, so you could focus more of your time and energy on making the one site better, instead of on site administration and duplication of efforts on two sites. Not to mention avoiding any risk of having the search engines think your two sites are an attempt to manipulate the rankings.
Remember the danger in comparing yourself to your competitor. You really, really don't know how well they are (or are not) doing. You can't see all the stuff they've got going on, so you're making assumptions based on very limited data (only what you can see publicly). it could be the part you can see is actually causing them problems and they're having to work like crazy behind the scenes to counteract the ill effects of a poor business decision.
Most importantly, assuming they are doing well, you have no way of knowing if they're doing well because of what you see them doing or in spite of what you can see. It's possible they'd be doing even better if they were to combine their two sites into one. It could be their "sister site" tactic is holding them back.
The point is: you don't know. You should never make a business decision based strictly on what you think your competitors are doing. Do what's right for your business, what fits best with your business model and your available resources.
It's OK to take a risk if there's a strong business justification for doing it. But if your only business justification is "the other kids are doing it," can you agree how silly that sounds?