I've jumped from Beta 9 to Beta 13 and I can no longer drag a web link from Internet Explorer into a map using the "insert a peer node" mode (Node should appear above the highlighted node). It does work if I use the "insert a child node" mode.
Interesting, I didn't realise that we could drag 'n drop browser links. That'll be a bit faster than copying 'n pasting.
However, in betas 9, 10, 12, 13 I get similar behaviour, the link is pasted showing the URL as the node text, and always as a child node, irrespective (as you said) of where the drop gradient suggests it'll appear. (Betas 9, 10, 12 don't actually create a link, just show the URL as the text in the node.)
FreeMind 080 behaves differently. It creates 3 child nodes, the page title as a text node, the URL as a link node, and a text node with the text "Link", with a child being another URL link node. That's choice for you!
I'm using FF 188.8.131.52 and have Java 1.6.0_02 installed courtesy of OOo
If we have a choice I'd prefer the page title as the node text.