No, I don't think so, yes they have a few key things in common being that they are both athletic, tomboyish and can sometimes get competitive but they have some equally crucial differences. Applejack is very mature and level headed, family oriented and for the most part tends to be confident and secure in herself. Rainbow Dash is often brash, reckless and arrogant. She also has some very deep seated insecurities about maintaining her rep and is reluctant to express the more feminine aspects of her personality (seriously addressing this issue would make an awesome Rarity and Rainbow Dash episode). To her credit Rainbow Dash has probably grown and matured the most out of the mane 6, especially in season 3 with her showing both a softer side in Sleepless In Ponyville and a responsible side in Wonderbolt Academy but these deep seated insecurities and other flaws while they have gotten better are still very much ingrained in her character.

 

One thing people have cited as a difference that I don't agree with is about Rainbow Dash being lazy, yes she take a lot of naps there is no doubt about it. But we have also seen multiple examples throughout the series of her training very hard in either competition or to meet her goal of getting into the Wonderbolts. I see Rainbow Dash as somepony who works hards hard and sleeps hard if that makes any sense.

 

Applejack and Rainbow Dash's relationship is like the opposite of Applejack and Rarity's relationship. Applejack and Rarity seem so different from each other but have a surprising amount of things in common which makes their interactions very interesting to me. Applejack and Rainbow Dash seem to have so much in common and they do but have as I have pointed out so many differences as well.

Source: Are Applejack's and Rainbow Dash's Personalities too Similar?