LED modulated @ high voltage -vs- constant @ low voltage
From the comments:

The peak forward current is what matters in this case. In most documents it is shown with a duty cycle of 10% @ 1KHz. The question remains though; if I drive an LED at peak forward current with PWM, will it be as efficient as a constant LED with same average wattage used?

It's not clear from your original post that that's what you are asking. It shows some confused thinking in your mention of doubling voltage.

Source: Purdue Engineering.
To answer your question you need to look at the relative luminous intensity vs. forward current on the datasheet. If it's linear then using PWM at \$n\$ times continuous reference current for \$ \frac {1}{n} \$ duty cycle will result in the same light output.
For the LED shown in Fig 1. indicates that there will be some reduction in light output if the current is pulsed as described in the previous paragraph.
Check the datasheets for the devices you are using.

Update 1
An article in LEDs Magazine titled Pulse-driven LEDs have higher apparent brightness makes interesting reading.

According to an article by Naoshige Shimizu of Nikkei Electronics, a research group at Ehime University, Japan, has developed a pulse drive control method to make LEDs look twice as bright by leveraging the properties of how people perceive brightness.
When a short-cycle pulse voltage with a frequency of approximately 60Hz is applied to an LED at a duty ratio of about 5%, the LED looks about twice as bright to the human eye in comparison with an LED driven by a direct voltage, the research group said.

And further down ...

There are two principles, the Broca-Sulzer effect and the Talbot-Plateau effect, involved in how human eyes perceive brightness. The Broca-Sulzer effect refers to a phenomenon in which light looks several times brighter to the eye than it actually is when exposed to a spark of light, such as a camera flash.
In addition, the Talbot-Plateau effect is a principle where human eyes repeatedly see flashes and sense the average brightness of the repeated lights. Until now, said Jinno, it has been believed that, due to the Talbot-Plateau effect, the brightness perceived by human eyes would not change even if an LED is pulse driven.