Lower bleph - which is a better option - having fat removed from inside lid or removed from under eyelash line?

Thank you for your question.
You are correct in that there are two different incision approaches when it comes to a lower blepharoplasty: transconjuctival and subciliary.  The choice of approach is highly dependent upon the patient's pre-op lower lid anatomy, most critically whether or not the patient has excess skin of the lower lid that will require excision.  
A transconjuctival incision is one that is made on the inside of the lower eyelid.  The primary advantage of this approach is that there are no external incisions, and therefore there is no risk of visible scarring, making this approach the patient favorite!  This approach is best suited for patients with primarily 'puffiness' of the lower lid, the result of an overdevelopment or pseudoherniation of fat.  Because this approach does not allow for removal of skin, this is not ideal for patients who have more than minimal skin laxity.
In contrast, a subciliary incision is an external incision that rests just below the lower lid lash line.  Due to its position, it tends to be very well hidden but there is always the possibility of a visible scar.  This approach allows the surgeon to address both the 'puffiness' and lax skin of the lower lids.
It would be important and recommended that you seek a consultation with a board certified plastic surgeon who is well-experienced in lower blepharoplasty procedures.  A consultation would be necessary to determine your candidacy for a lower blepharoplasty and to elucidate which approach would be of most benefit for you.  In my practice, I do prefer utilizing the transconjuctival approach, however, in some patients a subciliary incision will be required to address any more than mild skin laxity.
I hope you find this helpful and I wish you all the best!

This is complicated topic based on a number of factors.  I have personally performed several thousand eyelid procedures (I have three today!)  Transconjunctival eyelid procedures are best for patients (sometimes younger) with limited skin laxity and mostly puffiness (pseudoherniation of fat). Advantage of this procedure is no external incision.  Disadvantage is that nothing is done to address the skin (although laser can be performed in the right candidate).Transdermal (subcilliary) eyelid procedures are excellent for addressing skin laxity and puffiness.  Even eyelid position can be adjusted if need be.  The results can be extremely dramatic and all aspects of lower eyelid aging can be addressed.  Disadvantages of this procedure include the incision.  That said, it is extraordinarily subtle and is nearly invisible after healing.Best of luck!