Short answer: no, there are some racial traits that are unique - only humans can get Teamwork and Leadership, only Klingons can get Warrior, etc. Other traits are generic and can be selected by anyone.
What are some of the abilities that the science vessels have?
Most of your abilities in space come from your bridge officers. Science vessels carry more science officers, and at higher rank.
Science vessels also innately have more power in aux, have better shields, and can target enemy subsystems. Other players can get Beam: Target Shields, Weapons, Aux and Engines as Lt. level tactical powers, but it occupies a skill slot on a bridge officer. Science ships get those attacks for free, though they're weaker than the bridge officer versions.
Science ships are supposed to be better at detecting cloaked ships, though I never noticed this.