From what I have found there are 2 studies that investigated this exact question, both of which were performed in 2017 and both where training volume was matched. Both studies   showed that if training volume is matched, both 1RM and Muscle size increases equally. However, I don’t think in a gym setting the person performing the lift will make it so the volume is matched and would opt for performing the same initial weight they would use in a straight set with the added drop set weight as extra volume. This would then lead to greater volume overall which multiple studies have shown will increase muscle size and strength greater.    
So, the short answer is, if performed as described above, yes drop sets will make it so you gain more size and strength than regular straight sets as the more overall volume is performed.
However, performing drop sets will tire you and your muscles out faster meaning you’re more likely to have bad form, decrease the weight you’re lifting or even drop a few reps nearer the end of your working sets meaning volume, and your gains may even decrease. Having good form is crucial if you want to get the best results out of all your hard work whilst simultaneously reducing the risk of injury. So, using drop sets and getting to the point of exhaustion where your form breaks down can not only be a waste but risky if the likelihood of injury increases, this is especially true when performing compound exercises where bad form almost always leads to injury. For this exact reason, I would avoid drop sets entirely when it comes to compound movements.
Drop sets with isolation exercises.
Not only are drop sets easier to perform during isolation exercises, moving a peg on the cable machine or quickly picking up a lighter dumbbell, they’re also where drop sets work the best and are where I would use them in my workout routine if I were to use drop sets at all. This is because it is usually easier to perform an isolation exercise with correct form even when the muscle starts to become exhausted, this is because a good form is usually controlled by other muscles surrounding the targeted muscle which won’t have been taxed as much.
Your body is also faster at recovering from isolation exercises as they only target an individual or small group of muscles meaning your body can spend more resources on repairing that faster compared to a compound exercise where multiple muscles need repair. This ability to recover faster means you can increase the volume and take the muscle in question closer to exhaustion each set and still recover fast enough to perform equally well on the next set. This means overall volume during isolation lifts will be higher leading to greater gains.
What to take away.
Drop sets have a time and a place, even though when the volume is matched they don’t offer any extra benefits (except for maybe time-saving) they are an easy way to add extra volume to your workout and see some potential extra gains if you can handle them.
I would avoid drop sets completely on big compound movements as to prevent a break down in form and to reduce the risk of injury. However, they have a place during isolation exercises to add extra volume to your training without extending your time commitment to the gym. If I was just starting off with drop sets I would first experiment with them during my last exercise in my workout as doing them early on may be too taxing and decrease the effectiveness of the rest of your workout.
 T. N. P. L. A. M. &. N. Atsushi Kubota, "Effects of drop sets with resistance training on increases in muscle CSA, strength, and endurance: a pilot study," 9 May 2017. [Online]. Available: https://www.tandfonline.com/doi/full/10.1080/02640414.2017.1331042. [Accessed 3 August 2018].
 V. A. U. A. Libardi, "Crescent pyramid and drop-set systems do not promote greater strength gains, muscle hypertrophy, and changes on muscle architecture compared with traditional resistance training in welltrained men," 27 Jan 2017. [Online]. Available: https://link.springer.com/article/10.1007%2Fs00421-016- 3529-1. [Accessed 3 Aug 2018].
 D. G. Baker, "10-Year Changes in Upper Body Strength and Power in Elite Professional Rugby League Players—The Effect of Training Age, Stage, and Content," 1 Feb 2013. [Online]. Available: https://insights.ovid.com/crossref?an=00124278-201302000-00002. [Accessed 3 Aug 2018].
 J. W. Krieger, "Single vs. Multiple Sets of Resistance Exercise for Muscle Hypertrophy: A Meta-Analysis," 1 Apr 2010. [Online]. Available: https://insights.ovid.com/crossref?an=00124278-201004000-00036. [Accessed 3 Aug 2018].
 D. O. &. W. K. Brad J. Schoenfeld, "Dose-response relationship between weekly resistance training volume and increases in muscle mass: A systematic review and meta-analysis," 1 Jul 2016. [Online]. Available: https://www.tandfonline.com/doi/abs/10.1080/02640414.2016.1210197?journalCode=rjsp20. [Accessed 3 Aug 2018].
 T. Amirthalingam, Y. Mavros, G. C. Wilson, J. L. Clarke, L. Mitchell and D. A. Hackett, "Effects of a Modified German Volume Training Program on Muscular Hypertrophy and Strength," 1 Nov 2017. [Online]. Available: https://insights.ovid.com/crossref?an=00124278-201711000-00021. [Accessed 3 Aug 2018].