I'm assuming that we are talking about being 'transformed' into an asari in our modern world. You would be the only asari on earth, but with your biotic implant installed.
Besides all the nice stuff you are able to (long life span, potential for high visdom, biotics, good looks) you would also run into some problems:
If you got sick our doctors wouldn't have the slightest idea what to do. I would imagine that scientists would like to study you/perform tests and that would properly result in some confrontations.
I don't remember if asari eat the same food as humans, but if they don't you would run into problems quite fast.
The long life span would also bring some negatives with it. There is a lot of war and cruelty during 1000 years, and you would experience all of it. If you would fine somebody to start a family with, you would outlive them 10 times. More pain.
Even though this might seem like a pessimistic look at it (I call it realistic) I would grasp the chance to be an asari without hesitation. They are just so amazing and I think the positives out weight the negatives by a lot.