Rose Tyler and Clara Oswald

I have been a fan of "Doctor Who" since November of 2006, when I watched the two part second series finale, "Army of Ghosts"/"Doomsday," in which Billie Piper's Rose Tyler was locked in a parallel universe, forever separated from her love -- David Tennant's Tenth Doctor.
Rose was always my favorite companion. I loved how flawed and human she was -- she'd do something incredibly brave and selfess one second and then in the next, she'd act like a selfish, spoiled brat. Her tragic love story with the Doctor was a key factor, too.
When Jenna Coleman's Clara Oswald was introduced in 2012, I liked her immediately. She was bossy and sassy and yet kind and gentle. During her 2 and 1/2 seasons on the show I developed a deep affection for the character -- I related to her in so many ways -- and she also became my favorite companion.
It wasn't until just recently that I started to see how similar both women were. For instance, both lost a parent (Rose lost her Dad as a baby, and Clara lost her Mum during her teenage years. Both companions have romantic feelings toward the Doctor, though Clara gets over her infatuation. Rose and Clara are both present during a regeneration, have to take charge when the new Doctor is out of sorts and are unsure of the new Doctor afterward. In "The Parting of Ways," the Ninth Doctor activates Emergency Protocol One and has the TARDIS return Rose home; the Eleventh Doctor does the same to Clara in "The Time of the Doctor." Luckily, both companions find their way back. The most important similarity between the two is that they both helped to heal the Doctor during a dark point -- for Rose, it was helping the Doctor recover from the Time War and destroying his planet and people; for Clara it was reigniting the Doctor's lust for life after losing Amy and Rory. Coincidentally, both companions are also crticized a lot online and disliked.
I love both characters equally; I see a lot of myself in them both.
Fun Fact: while the characters of Rose and Clara never appeared in an episode together, both Jenna Coleman and Billie Piper appeared in the 50th Anniversary special "The Day of the Doctor." Coleman appeared as Clara, but Piper played The Moment, the physical embodiment of the weapon that the War Doctor used to destroy his planet, Gallifrey.