Question is, what does this do to search engine indexing, if anything? Do the major search engines like this kind of url?

Here is the answer of the "most major" search engine.

Perhaps the search engines prefer nice, ordinary urls like http://www.my_domain.com/aid_xxx_bid_yyy.htm

First ask yourself what's best of the user. IMHO the example without URL parameters looks nicer, and is friendlier to the user.

Second point is, just because the URL has no obvious params and ends with .htm doesn't mean it has to be a static page. What I'd do is to use the URLs ending in .htm(l), but still generate them dynamically. Either by having an script that handles all requests and looks at path_info, or with mod_rewrite.

I don't see how the underlying template engine affects this decision at all.