Multiple Sites Penalty

Is it possible to be penalized for keyword SERP if you have more than one site with similar content or structure. I moved my smaller site from Yahoo store to main site's server/host/platform which has same layout and same products offered (although copy is slightly different). Should I kill the other site or move it to another platform?

Yes you can be penalised for duplicate content.

Presumable you now want your new site to get the traffic?
If so, then ideally what you should do is redirect (301) the old site to the new one; that way you will avoid a duplicate content penalty and retain your traffic, and - after a period of time - you will get (almost full) credit for your existing backlinks.

If Yahoo won't allow that, you could add
to your old site pages (header section), then link to your new site pages from those pages (near the top of the page, old version => new version)... Beware though! Your old site will disappear from the rankings almost immediately, and - 'though the new one will gradually climb because of the links, it may take a while - and a lot more work - to regain your previous rankings.

Actually, they are different themes (just have overlap of products). I dont want to lose serp rank on existing sight more than recently converted one. My question is really - does older site get affected by new one.

If both sites have unique content, you should be ok. But then again, there are many other variables to consider. Is one a doorway site to the other? Are the product pages and their content identical? Are they both hosted on the same ip? etc. etc.

Without knowing much, I suggest focusing your energy on 1 website, if they're the same products. You're splitting your energy in 1/2, and that will leave you short in the end when put next to a competitor that has 1 site with full energy.

Most definately yes, to avoid it use no_index on your other site.