After many years (decades really) of shooting compounds here is my thought on rests; and I've used many different styles including drop aways.
Drop aways have become popular because so many people don't know how to tune their equipment to alleviate fletching contact with the rest. That and these shorter, higher profile vanes being used (Blazers, eg.).
If you are shooting a prong style or other conventional rest and can tune your equipment so there is no fletching contact issues then there is no need for a drop away other than to satisfy your need to part with money and/or impress other people.
I have found, after trying 9 different droppers, that the bow can gain some speed due to less friction, but it is very minimal. Some pitfalls of drop aways are that they msut be set up with proper timing so that they "drop" in time for the fletching to clear, but not so fast that they don't support the arrow. Once set up they work well so long as your string/cable(s) don't change length (creep or stretch). If the string cable stretch then this alters the timing of the rest as does any slippage of the cord attached to the dropper. These aren't major issues if you happen to know how or learn how to adjust them, but just some food for thought.
A conventinal rest such as your QT or something like a Star Hunter are pretty simple. You mount them to the bow, adjust them where you want them, and tune the bow/arrow combination to get the best arrow flight and fletching clearance. Once this is achieved all you need do is shoot your equipment.
If you ever get the chance take notice of what most of the real Pros and better target shooters have n there bows. In most cases you're going to see some sort of blade or other simple rest. There's a reason for this. Complete simplicity. Once tuned and locked down nothing can change because there are the least moving parts. Most apply the idea of KISS (Keep It Simple, Stupid).