How to compare two jquery ui autocomplete combobox values, not input values that are generated by jquery but <select><option value="foo"></option></select> values? How to get this values and compare them, everytime they are changed, either one of them?

I did not reallt understand your question correctly the first time.
I suppose you took the combobox code from the jQuery UI Autocomplete demo page ?
If you look at the code, it triggers an event “selected” when a selection happens:
As the combobox example uses the jQuery UI Widget Factory, you can easily bind an event handler for this event from the options when initializing the plugin instance:
This will act as sort-of “change handler”. In it, you have access to the value through
ui.item.value.Working example on jsfiddle.