Carpe Diem or Memento Mori?

Both statements can be seen from a Buddhist perspective. Though I would say rather than"seize the day" "seize the moment" would be better suited, being conscientious of every moment and experience is a foundation of mindfulness. As for remembering that we will die, and could die at any second is not just a fundamental understanding of Buddhist paths, it is one of the 3 marks of existence.

However your question didn't really make any sense.

There's "Memento Mori!".

“And for the sake of what benefit should a woman or a man, a householder or one gone forth, often reflect thus: ‘I am subject to death; I am not exempt from death’? During their lives beings are intoxicated with life, and when they are intoxicated with life they engage in misconduct by body, speech, and mind. But when one often reflects upon this theme, the intoxication with life is either completely abandoned or diminished. It is for the sake of this benefit that a woman or a man, a householder or one gone forth, should often reflect thus: ‘I am subject to death; I am not exempt from death.’
AN 5.57

The next version is "Memento Mori, therefore Carpe Diem!"

“This noble disciple reflects thus: ‘I am not the only one who is subject to death, not exempt from death. All beings that come and go, that pass away and undergo rebirth, are subject to death; none are exempt from death.’ As he often reflects on this theme, the path is generated. He pursues this path, develops it, and cultivates it. As he does so, the fetters are entirely abandoned and the underlying tendencies are uprooted.
AN 5.57

And there's also "Carpe Diem anyway, don't waste your life."

Those who in youth have not led the holy life, or have failed to acquire wealth, languish like old cranes in the pond without fish.

Those who in youth have not lead the holy life, or have failed to acquire wealth, lie sighing over the past, like worn out arrows (shot from) a bow.
Dhp 155 - 156

The exact advice to be given is like medicine. Each medicine is suited for a different illness. Depending on one's addictions, motivations and level of energy, one of the three above should be chosen.

I suppose those are two sides of the same message.

You can find both in the suttas, for example:

• Momento mori

  "If, lord, such a great peril should arise, such a terrible destruction of human life — the human state being so hard to obtain — what else should be done but Dhamma-conduct, right conduct, skillful deeds, meritorious deeds?"

  "I inform you, great king, I announce to you, great king: aging and death are rolling in on you. When aging and death are rolling in on you, great king, what should be done?"

  Pabbatopama Sutta: The Simile of the Mountains (SN 3.25)

• Carpe diem

  Here are the roots of trees. Here are empty places. Get down and meditate. Don't be lazy. Don't become one who is later remorseful. This is my instruction to you.

  Bhikkhunupassaya Sutta: Directed and Undirected (SN 47.10)

  "It would be a sheer coincidence, lord, that the blind sea-turtle, coming to the surface once every one hundred years, would stick his neck into the yoke with a single hole."

  "It's likewise a sheer coincidence that one obtains the human state. It's likewise a sheer coincidence that a Tathagata, worthy & rightly self-awakened, arises in the world. It's likewise a sheer coincidence that a doctrine & discipline expounded by a Tathagata appears in the world. Now, this human state has been obtained. A Tathagata, worthy & rightly self-awakened, has arisen in the world. A doctrine & discipline expounded by a Tathagata appears in the world.

  "Therefore your duty is the contemplation, 'This is stress... This is the origination of stress... This is the cessation of stress.' Your duty is the contemplation, 'This is the path of practice leading to the cessation of stress.'"

  Chiggala Sutta: The Hole (SN 56.48)

"Momento mori" tries to make people dispassionate about worldly gain -- to cease, to discourage.

"Carpe diem" tries to encourage people to take the opportunity to practice -- to begin, to continue.