Well... in the long run, the winner will be... France!
This was a huge factor in the OTL situation actually; the Spanish plan was to create a puppet monarchy via the Catholic League--either the current monarch would be cowed, or they'd put in a new one.
My go-to source on this is
The Armada, by Garrett Mattingly (Houghton Mifflin, Boston 1959).
The most important single lesson from the book: The English had superior guns. And Spanish captains and I suppose sailors knew this too. English ship cannon had longer range. They learned, over the course of the encounter, that they could not stand off so far as to be safe from Spanish return fire (the Armada, by the way, was actually pretty multinational in its crews and hulls, using Portuguese as well as a single grand Venetian galleon (basically confiscated) and perhaps some others in the mix too) but still, if they came in close enough for really devastating firepower on the Armada ships, the Hapsburg expeditionary counter fire was considerably less damaging to them. No way to win without getting bloodied (they tried that first, albeit with some disruption by captains keen on prize-taking).
Also the English were defending, and deployed close to their supply bases--which got overwhelmed, but the Spanish had to sail for a very long time to reach England, and had short and bad supplies. Both sides used up ammunition a lot faster than they estimated they would, but the English could do something about that.
If I recall Parma's attitudes correctly, what he believed was that the Hapsburg Empire should concentrate on conquering the Netherlands first, and then, with commandeered Dutch hulls and crews, and more importantly without these skilled and apt sailors with their light ships very well suited to Channel waters being on the hostile side hemming in Imperial options, invade England after the fall of the Dutch. And considering the huge amount of money King Philip spent on the Armada, it seems plausible to me that if that same money had gone to the enterprise of subduing the Lowlands completely, Parma could have accomplished it and then, using ships superior for the purpose over a much shorter range, and with the interdiction of the former Dutch enemies eliminated, managed to land sufficient troops in England.
The question of whether Protestantism could ever be fully suppressed in England might be the ultimate downfall of Hapsburg-puppeted England, but there most certainly were a whole lot of Catholics in England, whereas the English armies would be no match for Parma's forces if he could only get them landed. They would count on a large rising of the English countryside in their favor. Quite a few nominal Protestants would surely shift back to Catholicism if Elizabeth were to be killed or exiled, and a coalition of Spanish forces (really, mercenaries, but paid by Philip and certainly including quite a few Spanish
tercios) and Catholic English held the upper hand. It would be entirely possible for a Catholic monarch to be conciliatory to Protestants and tolerate them, those willing to submit anyway, reserving fire and terror only for those who would not. Now in the long run this might or might not stabilize, but in the short run--Elizabeth could not last long, not as ruling queen anyway, if only those Spanish armies could land.
The Armada plan as approved was doomed I think, but I do suspect that a heavy surge to break Dutch resistance followed, within just a few years at most, by invasion across the Channel from the Netherlands could have worked. The trouble with that was that Philips's pretext for invading was the execution of Mary, and he had to show that Elizabeth would be punished for that directly and immediately, not as something that might happen half a decade or so hence. Also the notion had arisen in some councils that it would be very difficult and perhaps impossible to defeat the Dutch rebellion as long as England was able to aid them. Parma was overruled, wrongly I suspect.
I believe Mattingly does address the incident where shifts of the wind did give the Armada some advantage, but dismisses it as temporary and non-decisive, for even if the Spanish took the best advantage they could English superior gun range would still make it chancy and costly for the Armada to decimate the English ships--whereas when the wind did shift, the Spanish would then be in dire straits indeed. I've found the book and skimming over the chapters again it seems this is pretty much the gist of it. The Armada was indeed more impressive and better organized than the English had anticipated, and staying at safe distances from Spanish counter-fire the English could do nothing to it--but they learned to come in closer, taking damage but dishing out more. Meanwhile if I have found the right passages, Mattingly dismisses the idea that the Spanish fleet could have either caught the English between sea and shore, or landed on England themselves--the necessary troops were in the Lowlands which is why Sidona's orders were to proceed there, to the Flemish ports, and cover their being ferried over.
Another possible divergence from OTL might be if Drake, and other English hotheads, had been given the leeway to indulge in aggressive schemes to attack Iberia in the hope of either decimating the Armada before it fully formed or diverting it to defend their homeland. In fact Drake had led such an expedition earlier, and Mattingly credits the greatest prize he won in raiding the Spanish and Portuguese coast as a large stock of seasoned wood, suitable for building storage casks for supplies; this was far too bulky for his raiders to bring home but instead it was burned up. Mattingly stresses very strongly the suffering of the Armada from supplies that went bad in green wood casks that were poor replacements for what Drake destroyed. But as the possibility of the Armada went from remote to imminent, Queen Elizabeth kept her sea dogs on a tight fiscal leash. This meant that the English, lying in wait in sight of their home shores, were to enjoy the strategic advantage of relatively easy and abundant resupply, and that the entire mass of English seapower would be amassed there. Drake and others wanted to venture out instead, and had they done so, they would have found no amount of mayhem on Spanish or Portuguese shores would divert Medina Sidona from his orders specifically forbidding him to be so distracted, and coming upon England guarded by a depleted and scattered fleet, might have been far better able to arrive at his appointed rendezvous intact. Englishmen fumed against their Queen's womanly "cowardice," compounded with penny-pinching, but in fact Elizabeth's strategic judgement appears to have been far superior to theirs. To make such a POD then, one either must have mass mutiny against the regal commands, or for Elizabeth to be browbeaten or beguiled into quite different decisions. These would be out of character.
Two more major issues, already touched on, cloud any possible Spanish victory. Parma was not disobedient to his orders in the grand plan, but he simply could not come up with suitable shipping for the necessary troops, nor could they expect to get across the channel without detection and decimation by screening Dutch patrols. Parma did not in fact control a suitable port to embark his legions.
His own idea as mentioned was that if the Empire had subdued the Netherlands first, the picture would be very different.
Then there is the question of whether English patriotism would trump the sectarian calculations of the Catholic invasion--patriotism both in the form of die-hard and fanatical resistance by English Protestants, and the question of how certain the Catholic and crypto-Catholic sectors of the countryside would be to rally to the foreign invaders. Again the character of Elizabeth herself is pretty pivotal.
My belief, no doubt strongly influenced by Mattingly, is that the consolidation of both these factors in England's favor, that is the ultimate failure of the Hapsburgs to take control of the Netherlands entirely, and the solidifying of English patriotism so that even Catholics could be relied upon to put country and crown first, were more products of the victory over the Armada than backstops against a failure. The failure of the Armada was a great breeding ground of patriotic myth in England, and reinforced the general progress of Elizabeth building up solid Westphalian nationality in her kingdom over her reign. And it also meant the Dutch would be reinforced by England still, whereas the Hapsburg empire was much exhausted from it, especially financially. Had it gone otherwise somehow, we'd find the English identity quite a different thing--surely not Hispancized, but not the nation Elizabeth bequeathed to James either. The Netherlands would probably have to be conquered before the invasion of England, and if by some bizarre miracle England could be conquered before the Netherlands were subdued, their fall would be in short order after the loss of their diligent protector/partner across the Channel.