Thanos and the Phoenix Force are two of the biggest threats the Marvel Universe has ever known. Anytime either shows up it becomes a massive battle for the fate of life itself, and as the comics upped the ante their antagonists posed over the years, both got increasingly powerful to ludicrous dimensions.
But which of the two stronger? Let's look at what each entity has to offer, looking at the worlds both have destroyed and the enemies they vanquished. Thanos may be obsessed with reaping death throughout the universe, but taking on the very embodiment of reincarnation is a tall task, even for the Mad Titan.
TITANIC POWER
Born to a race of godlike beings on Saturn's moon Titan, the destiny they lay ahead for Thanos since his birth was always meant to be one of utter destruction. After a lifetime of suffering and persecution, he eventually embraced such a destiny, literally worshipping the embodiment of Death and becoming determined to offer the universe to her as a sacrifice. Unfortunately for the universe, he's powerful enough to do it.
Thanos commands a tremendous strength that has broken apart entire planets in the course of his fights. What's more, his abilities stretch beyond the purely physical to the command of matter itself, turning organisms to stone or stopping Mjolnir in mid-air with but a thought. Thanos' thoughts are a dangerous thing, as he is one of the mightiest telepaths in the cosmos, welding one of the most impressive minds to ever set its sights on the demise of all life.
A (PHOENIX) FORCE TO BE RECKONED WITH
Manifested as the embodiment of life itself and serving as a nexus to all psionic energy in the universe, the Phoenix Force is not so much a being as an entity. Although its history dates back countless millennia to the inception of the stars, it solidified a place in Marvel Comics history during the Dark Phoenix Saga after taking Jean Grey as its host.
The Phoenix Force would claim many other hosts over the years, and it could often be difficult to separate its powers from those it amplifies from its host body. Regardless, in any incarnation, the Phoenix Force commands immense telekinetic and telepathic energy, manipulating such gargantuan energy that it could drain the Sun of its spark. Endlessly reincarnating after its every defeat, it's hard to imagine that any force could be so strong enough to put it down permanently.
AN EPIC CLASH
In analyzing how the two fighters stack up against each other, the clash would seem to be a case of comparing two infinities to decide which is larger. The power commanded by both Thanos and the Phoenix Force exists on such a ludicrous scale that the feats themselves are hard to compare, but luckily for fans idly wondering about their matchup, the fight is not without precedent. In Thanos #11, the Mad Titan's spurned son Thane claims the Phoenix Force for a weapon against his father, and the two duke it out in a clash that devastated the planets they strove across.
While the fight itself might seem inconclusive (Thanos directed the battle to the God Quarry where the Phoenix Force was banished from Thane's host body), there were some key points that stand out. The first is that the two were explicitly equally matched throughout the fight, with neither able to gain an edge. Despite that, it's important to remember that Thanos was actually weakened during the fight -- striking the Mad Titan at his weakest was Thane's whole plan. And yet even then, Thanos managed to turn the fight to his advantage, utilizing his environment and keen intellect to gain an upper hand.
The fight may have gone differently with a different host body, as Thanos noted that Thane did not know how to wield such godlike power, but nevertheless the advantages were still on the Mad Titan's side. Being a force of nature may speak to the raw power of the Phoenix Force, but when it comes to winning a fight like this there's nothing you can rely on more than brute strength. Thanos takes the win here and might crack a smile while doing it.