Not eating before a workout will technically dip into your reserves more, but it tends to burn more muscle than fat.
These numbers are just theoretical for simplicity, the actual math per individual person goes way deeper

Lets say you went for a run without eating and you burnt 500 calories.
If you had eaten a meal of around 250 calories, you would have only burnt off 250 calories from your run.
So at first glance, it looks like not eating would get you faster results.
If you have not eaten, the body has no immediate energy to feed off - and like I said before, muscle is easier and faster to break down than fat. Your body heads to the muscle, burning off what you worked so hard to build up. So most of that 500 calories you burnt off during the run will have came from your muscle - lets say a 60-40 split.
So you will have burnt off 300 calories worth of muscle and 200 calories worth of fat. Taking the numbers from before with 4 calories per gram of protein (muscle) and 9 calories per gram of fat. That works out to 75 grams of muscle burnt and 22.2 grams of fat.
If you have eaten, the immediate energy will come from the glucose energy stored inside your muscles from the meal you previously ate. Your body will not be forced to eat in to your muscle, you will also be able to work out for longer at a more optimum rate because you've fuelled your body before hand. So this time lets assume a 60-40 split in the opposite direction - bearing in mind we've only actually burned 250 calories this time and the other 250 came from the meal.
150 calories worth of fat and 100 calories worth of muscle were burnt. That's 16.6 grams of fat burnt and 25 grams of muscle.
For a slight sacrifice in fat burnt we've massively reduced the amount of muscle burnt during the workout.
Now here's the kicker that is hard to measure except under lab conditions: After a work out your body is a fat burning furnace, and the more muscle you have the more fat you will be burning during "down time"
Lets say that in a regular three hour time stretch your body would burn 250 calories (basing this on the governments average figures for the female bodied, it will be more if your male bodied/on T) - after a workout we can say you burn 150% of your average. So for three hours after your workout you've burnt an extra 375 calories. The vast majority of this will be from your fat, because it's a slower burning energy that feeds everything during downtime, organs etc. Lets say 80-20
Put it all together - for the workout + the 3 hours downtime you will have burnt:
Not eating: 875 calories - 55.5 grams of fat and 93.75 grams of muscle burnt
Eating: 625 calories - 49.9 grams of fat and 43.75 grams of muscle burnt
For almost the same amount of actual fat burnt you have burnt less than half the amount of muscle.....and in the long term that muscle will help you burn more calories during down time.
This is without adding in the variables from the fact that eating in general stokes your "fat furnace" a little bit anyway; and the fact that you will be able to work out longer and harder if you've eaten (and thus burn more calories in general) - so that 49.9 grams of fat burnt is an absolute minimum, the actual number will be higher.
I hope this wasn't too rambly, I could talk about this stuff all day long

TL;DR: If you eat before a workout then overall you will burn more fat than if you didn't