In general, throughout the war, the Waffen-SS (W-SS) received better equipment and training which gave them at least the aura of "elite status". However, neither of these things automatically results in superior effectiveness in the field. I would argue that until around 1940, the W-SS did embody a position as a showpiece formation but they were not the super humans that film and TV often make out. From the Nazi point of view, their elite station was thanks to their strict racial rules which ensured only the "greatest" Aryans were accepted but that does start to change later in the war.

Hitler allowed the SS to be militarised from 1935 onwards which led to guarantees on certain equipment and a more rigourous training programme. SS-W units had joined the march into Austria and Czechoslovakia which was a walk in the park (though there were some grumbles about W-SS inability to understand large scale operations) compared to the invasion of Poland where they faced actual resistance. During the Polish campaign, Army staff complained that W-SS units were willing to take far too many casualties and did not grasp the concept of combined operations with the Heer. Of course, there was certainly some tension between OKW staff and senior SS men but the casualty list speaks for itself. I would add the SS retorted by saying Heer Generals kept them very much in reserve and prohibited them from training in a divisional context which does seem accurate. For a modern army to work, especially in the context of the Polish campaign, it is absolutely necessary for the two branches to function and collaborate in tandem (think of it as the Army working with the Navy or Air Force). You cannot be an "elite unit" if your branch is unable to work strategically with the other.

Despite these disagreements and the W-SS’s overall average performance in Poland, their position in the Nazi state left them immune to this sort of criticism and actually received more detachments as a result.

I don't want to go through every engagement SS units fought in but the Invasion of France highlights a number of issues, even when fighting the beleaguered BEF and Dutch Army. On multiple occasions, W-SS detachments were subject to brutal counterattacks from British and Dutch forces and were repeatedly beaten back or failed to react accordingly. In one instance a SS General was killed after foolishly standing in a window during a firefight with Dutch troops and General Dietrich was forced to cover himself in mud and hide in a ditch to escape British troops after an unauthorised attack went south leaving him vulnerable.

The biggest change in the effectiveness of the W-SS came in tandem with the declining chances of victory. Non-Germans were initially not targeted for recruitment until other "Aryan stock" like Danes and Swedes were offered places. These "foreign legions" quickly diminished thanks to the colossal casualties incurred on the Eastern Front and their inability to fill the gaps. Instead, other occupied territories like Yugoslavia and Romania were targetted thanks to large (supposed) ethnic German populations there. By no means did the fighting status of the W-SS specifically decline further thanks to the influx of non-Germans, but their inexperience and lack of training were fundamental.

In many cases SS officers could not always communicate with their new troops or had zero understanding of their culture which they held in disdain, this was particularly apparent when Bosnians were recruited. The actual units themselves were certainly of dubious capability when many had been pressganged into them. The Dirlewanger Division in particular extended its recruiting arm to Soviet POWs, political prisoners, and convicted criminals as an opportunity for freedom outside of the camps- hardly a dedicated force of experienced veterans.

In 1940 the W-SS consisted of just over 90,000 men. By the middle of 1944, it had almost 600,000 in its ranks with half of that figure from non-Germanic countries. Even at the outset of the war, the W-SS was by no means the creme de la creme of the German military and as the conflict dragged on their capacity declined even further. Few new recruits joined out of genuine dedication to the fascist cause and were more often there out of fear or ulterior motive which is far from the qualities of a supposed elite army. The only practice in which the SS as a whole excelled in was not combat effectiveness or strategic wizardry, but cold blooded murder and brutality.

(Thank you to Adrian Weale's book The SS: A New History for some of the specific examples made above)

Edit, spelling error.