На angularJs версии 1.5 вариант работы такой:
Plunk - Используйте angularJs 1,5x
<select class="form-control" ng-model="data.items[$index].selectedBusinessType.id"
ng-disabled="item.CanChangeBusinessType"
ng-change="changeBusinessType(item, selectedBusinessType.id)">
<option ng-repeat="businessType in item.businessTypes" ng-value="businessType.id">
{{businessType.id}}
</option>
</select>
Но это не работает в версии 1.4+.
Plunk - Используйте angularJs 1,4x
<div>
<select class="form-control" ng-model="data.items[$index].selectedBusinessType.id"
ng-disabled="item.CanChangeBusinessType"
ng-change="changeBusinessType(item, selectedBusinessType.id)">
<option ng-repeat="businessType in item.businessTypes" ng-value="businessType.id">
{{businessType.id}}
</option>
</select>
</div>
Второй сработавший вариант - используйте ng-option:
Ng-Option с использованием
<select class="form-control" ng-model="item.selectedBusinessType"
ng-options="option.id as option.name for option in data.businessTypes"
ng-disabled="item.CanChangeBusinessType"
ng-change="changeBusinessType(item, item.selectedBusinessType, '{{item.selectedBusinessType}}')">
<option value="">-- Не указан --</option>
</select>