I wouldn't exactly say that Alexandra was more emotional than Tatiana, but perhaps Alexandra showed her emotions a lot more, and Tatiana didn't weighed down by feelings. A lot of people said that Tatiana was a perfect reincarnation of Alix, both physically and spiritually. They certainly both were enigmatic, in my opinion, and had a strong sense of duty and religion, and were unmistakably royal.
As for looks, there have been very few occasions that I've noticed a strong resemblance between Tatiana and Alix, but I've often felt that Tatiana looked more like her father, particularly the eye shape, but I'd say the nose is exactly like Alix's. Overall, Tatiana resembled both of her parents, in my opinion.