Free-Weights = 10.4kcal, Machines = 8.9 kcal, Incorporating Cardio in a Weight Training Circuit = 13 kcal/min Burned

This article is not supposed to encourage the use of exercise as a means to eat more junk. After all a psychotherapeutic / psychiatric ward is the only place this form of exercise addiction is going to get you.

Ok, let me briefly make one thing unmistakably clear: you should never train to burn calories (even worse, to eat pizza and pie, because you "deserve it"). Good reasons to train are (a) to build muscle, (b) build strength, (c) improve your conditioning and (d) general health. It is likewise a good idea to (e) support your dieting efforts with strength and cardio training that is meant to increase the rate of fat/muscle loss.

Yet even if you don't train to burn calories, it can be very useful in all these contexts to have at least an estimate of how much energy you're spending during the workouts. What for? Well, to know roughly how much more you'd had to eat to stay in an energy and how much more would be too much so that fat gain would be the inevitable consequence.
Speaking of energy balance(s), you should also be aware that your body will adapt to chronically reduced energy intakes. In other words: If you have been dieting for say 8 weeks, it is not unlikely that you are spending slightly, but statistically significantly less energy for the same workout (15 reps 70% of 15 RM, 2 s:1 s cadence; 45 s per exercise; only 15 s of "rest" = moving to the next exercise | running during the CE was performed at 70%  | the total duration of one lap of the circuit was 7 min and 45 s, for the total time the subjects actually worked out (not how long they were in the gym, it was 3x 7:45 = 23 min and 15 s | see Figure 1).

Figure 1: Overview of the standardized circuit resistance training protocols in Benito, et al. 2016.

This, as well as the individuality and the fact you are no identical clones of the 15 men and 14 women aged from 18 to 28 years, who participated in a recent study from the Technical University of Madrid (Benito. 2016), renders the absolute energy expenditures I've plotted for you in Figure 2 relatively meaningless (note: the subjects were pretty active, with of exercise 3-5h/week - better than your average study subjects).

Figure 2: Net energy expenditure (Kcal) in men (n = 15) and women (n = 14) during the entire circuit weight training protocol (Benito. 2016) - Percentages represent the individual contribution of aerobic energy expenditure (gray) and anaerobic energy expenditure (black) to total energy expenditure. CM: Circuit Machine training protocol; FW: Free Weight-training protocol; CE: Combined Exercise training protocol. a p<0.05 with CM, b p<0.05 with FW, ** p<0.001.

As you can see in Figure 2 the analysis of the data that was acquired during the three standardized circuit resistance programs (see Figure 1), show that...

• the combined resistance + endurance training regimen (CE, exercises see Figure 1, bottom), with 13kcal per minute (8.4 kcal/min in women), was by far the most energetically demanding (is also had the highest fat/glucose oxidation ratio, meaning more workout fuel came from fat - not necessarily body fat, though - in CE) and that 
• free weight (FW) training, with 10.4kcal/minute (6.4 kcal/min in women), was more demanding than machine-based circuit training (CM), with only 8.9 kcal/minute (5.4 kcal/min in women).

Figure 3: Physiological parameters (mean±SD) measured during Circuit Machine training protocol (CM), Free Weight training protocol (FW) and Combined Exercise training protocol (CE) - data expressed relative to arithmetic averages for VO2, RER, LA- and RPE; thus 9% reduced RPE in CE mean that CE is 9% less fatiguing than the avg. of all tested workouts.

References:

• Benito, Pedro J., et al. "Cardiovascular Fitness and Energy Expenditure Response during a Combined Aerobic and Circuit Weight Training Protocol." PLOS ONE 11.11 (2016): e0164349.