[SalesForce] Checking if field has changed

I need to check that a picklist field = "Active" and that it's previous value did not equal "Active" (only need to fire when this one field has changed). I am attempting to do this with the following line:

if (P.Project_Status__c == 'Active' && P.Opportunity__c != Null && oldProjectMap.get(P.Project_Status__c) != 'Active')

But am receiving the error: "Comparison arguments must be compatible types: Project__c, String"

What am I doing wrong?

Below is my entire class

public class ProjectUtil {
    public static void UpdateOppStage (List<Project__c> Projects, map<id,Project__c> oldProjectMap) {
        Set<Id> ActiveProjectOpps = new Set<Id>();
        Set<Id> CompleteProjectOpps = new Set<Id>();
        //update
        if (oldProjectMap != null){
            for (Project__c P : Projects) {
            if (P.Project_Status__c == 'Active' && P.Opportunity__c != Null && oldProjectMap.get(P.Project_Status__c) != 'Active'){
                ActiveProjectOpps.add(P.Opportunity__c);
            }
            else if (P.Project_Status__c == 'Complete' && P.Opportunity__c != Null){
                CompleteProjectOpps.add(P.Opportunity__c);
            }   
        }
        }
        // insert 
        else if (oldProjectMap == null){
            for (Project__c P : Projects) {
            if (P.Project_Status__c == 'Active' && P.Opportunity__c != Null){
                ActiveProjectOpps.add(P.Opportunity__c);
            }
            else if (P.Project_Status__c == 'Complete' && P.Opportunity__c != Null){
                CompleteProjectOpps.add(P.Opportunity__c);
            }   
        }
        }

        List <Opportunity> ActiveOppsToUpdate = [SELECT id, StageName FROM Opportunity WHERE id in:ActiveProjectOpps];
        List <Opportunity> CompleteOppsToUpdate = [SELECT id, StageName FROM Opportunity WHERE id in:CompleteProjectOpps];

        for (Opportunity item: ActiveOppsToUpdate){
            item.StageName = 'Delivery';
        }
        for (Opportunity item: CompleteOppsToUpdate){
            item.StageName = 'Post Delivery Internal Meeting';
        }

        update ActiveOppsToUpdate;
        update CompleteOppsToUpdate;
        }
 }