If it is just a simple text property it is probably easiest to write some code directly in the item template, or create a method in codebehind to which you pass the Container.CurrentPage for processing.

If you really want to use the property control you can do something similar by putting your logic in a method which returns the property name. I haven't tried this, but I thing it might work.

<EPiServer:Property PropertyName="<%# GetPropertyName(Container.CurrentPage) %>" runat="server" />

in codebehind:

protected string GetPropertyName(PageData page) { // logic which selects property name goes here}

Or directly in markup with fallback from MenuTitle to WindowTitle for example:

<EPiServer:Property PropertyName="<%# Container.CurrentPage["MenuTitle"] == null ? "WindowTitle" : "MenuTitle" %>" runat="server" />