I simplified the test case further and started with the non-modal popup. It seems that the culprit for the Close button not working on the draggable is the type="button" attribute. Removing this seems to make the "Close" button work again. In checking the 1.5.3 release, that attribute is in the component-showcase example for popups but has since been removed. The spec for command button says that the only valid values are "submit" (the default) and "reset". In any event, the draggable popup seems to work as advertised in the test portlet when the suggested changes is made.
The modal dialog code didn't have the type attributes set for the close button so didn't show the issue. I tried putting two instances of the test portlet on the same page and, once the above changes was made, both types of popup panels appeared to work as per the component showcase example. There may still be some work around how popups should be "owned" by the portlet that spawns them (e.g. should a modal popup be modal for the whole page or should it just be model for the parent portlet) but that discussion should probably be done elsewhere. At this point, it appears that popups generally work in Liferay.
icefaces-test-popup-portlet.war