For most people who grew up in Western culture, the story of Sleeping Beauty is fairly common-place. At the very least, the basics of the story are widely known from the ballet, books, and movies (including the disney version). The section of Sleeping Beauty that pertains to Sailormoon is specifically the beginning:

Once Upon a Time there was a King and Queen who were without child for a many years. This was very sad to the couple, until one day, joyously, the Queen gave birth to a baby girl.
The King and Queen were overjoyed, and to celebrate decided to throw an elaborate christening for the child. The couple made sure to invite seven faeries from all over the land, knowing that they would bestow great gifts upon their new daughter.
Once the party had begun, however, an uninvited guest appeared to celebrate as well. Another faerie, who the King and Queen had overlooked to invite, believing that she was long dead, appeared. Feeling that the lack of invitation was a slight, she placed a heavy curse on the new born baby as her gift to the child, promising that the child would prick her finger on a spinning wheel and die by the time she was just sixteen...

There are, of course, variants to this tale. In some versions, the faerie is slighted because, while welcome, the place setting she receives isn't as nice as the other faeries who had golden dishes made for them specifically. In some versions, the lack of appropriate place setting is why the King and Queen do not invite the final faerie in the first place. These discrepancies are unimportant when comparing it to Sailormoon. What is important are these facts:

The event is to celebrate a newborn baby

There is an uninvited guest, a woman of great power

The guest gives the gift of a curse upon the child that will be fulfilled before she reaches adulthood.

In Sailormoon, the Dream Series of the manga, this storyline is echoed in the origin tale of Queen Nehellenia. In it, during the past Queen Serenity has just given birth to a daughter. The four inner guardians arrive to celebrate the new birth and promise to protect her. As they are celebrating, from the shadows creeps in Queen Nehellenia to crash the party. The senshi are notably upset at this and even call her an uninvited guest. Queen Serenity extends the invitation for Nehellenia to stay- on the condition she is not to bring darkness or evil with her. Nehellenia argues that light is attractive to darkness, and vice versa. Queen Serenity then uses the power of the maboroshi no ginzuishou to seal Queen Nehellenia into a mirror, and as she is sealed away, Nehellenia says her gift to the new Princess is her curse- that the whole kingdom will fall and she will die before she has ascended the throne as queen.

The parallels are very close and unmistakably similar.

Source Materials:
Grimm's Faerie tales; The Annotated Sleeping Beauty; Bishoujo Senshi Sailormoon Manga Volume 15