As I ranted about before (Ability Sequence Notes), E is, in my opinion, a better first max than Q. And if you have the Rylai's, the E max, hit your W into your E, and follow up with the Q, Taliyah can be an amazingly bursty mage. With Rylai's and her ult, she can chase down anyone. She will always be difficult of course because she has quite a number of skill shots, but with the added slow, it's almost a piece of cake.

Now, I know that E is a shorter range than Q, but missing your Q has much bigger consequences than missing your E (zoning control of E), so you really do have to have enough health or be tanky enough to survive the fights long enough to inflict a lot of damage. But E is barely any shorter.

The biggest problem I found with Taliyah that made me switch over to maxing E? Her worked ground. Yes, worked ground is nice for the movement speed, but if your lane is absolutely covered in it, you cannot do enough damage to your enemy, should they dive you. Or if it's the perfect time to Q, have them in a corner under their tower, they're low on health, but worked ground is everywhere or you forgot/accidentally stand on the ground, you might be the one who gives up their life.