I have two insert statements, almost exactly the same, which run in two different schemas on the same Oracle instance. What the insert statement looks like doesn\'t matter - I\'
The first thing to realize is that, as the documentation says, the cost you see displayed is relative to one of the query plans. The costs for 2 different explains are not comparable. Secondly the costs are based on an internal estimate. As hard as Oracle tries, those estimates are not accurate. Particularly not when the optimizer misbehaves. Your situation suggests that there are two query plans which, according to Oracle, are very close in performance. But which, in fact, perform very differently.
The actual information that you want to look at is the actual explain plan itself. That tells you exactly how Oracle executes that query. It has a lot of technical gobbeldy-gook, but what you really care about is knowing that it works from the most indented part out, and at each step it merges according to one of a small number of rules. That will tell you what Oracle is doing differently in your two instances.
What next? Well there are a variety of strategies to tune bad statements. The first option that I would suggest, if you're in Oracle 10g, is to try their SQL tuning advisor to see if a more detailed analysis will tell Oracle the error of its ways. It can then store that plan, and you will use the more efficient plan.
If you can't do that, or if that doesn't work, then you need to get into things like providing query hints, manual stored query outlines, and the like. That is a complex topic. This is where it helps to have a real DBA. If you don't, then you'll want to start reading the documentation, but be aware that there is a lot to learn. (Oracle also has a SQL tuning class that is, or at least used to be, very good. It isn't cheap though.)