This is an on-going debate. Essentially it matters pretty much not at all so long as the machines aren't miserable. Miserable in this case meaning two things: first that the angles you're forced to work through aren't uncomfortable, and second, that the tension isn't applied at wrong times.
Let's play out the first one: comfort. Injury susceptibility is just as much a factor here as muscle functionality. If it feels awkward and you can't adjust the height and/or seat placement in a way to remedy that awkwardness, it's probably a piece of trash. You're not going to effectively work any muscle group while being subjected to a good chance of injury. There's a lot of these machines. However, if it feels comfortable, it's probably fine on these terms. There's a lot of these too.
As far as the other terms, the application of tension is the issue. The two consistent problems are poorly designed varied resistance, or just a shitty, choppy range of motion. I feel the latter is obvious enough to bypass the explanation. Differentiating the resistance can be a complicated issue though. Nautilus made this up originally, and it's pretty clever. In the old machines, they just worked with a pulley-system that kept the tension constant clear through the entire range of motion. However, your muscle is stronger and weaker at different moments within the range of motion for both mechanical and physiological reasons. Mechanically, it depends on your body's relative position to gravity, joint angles, lever issues, Newton's laws, etc. Physics. It deals with physics.
Physiologically, your muscle has a point about half way through the range of motion where you're stronger than you would be in a more contracted or more extended state. This is because the contractile proteins that cause your muscle flexion are lined up ideally. Extend your muscle more and they can't reach each other well enough to contract. Flex your muscle more and they get all cramped up and can't generate as much force.
So the underlying philosophy of varied resistance is that you can make a machine to match the strength abilities of the muscle throughout the entire range of motion. At the strongest point, the weight is heaviest, and at the weaker points, the weight is lighter. So Nautilus made the first machines to change the tension developed mechanically to match what your muscle is capable of physiologically. With this method, the weight should start off fairly light, become heavier in the mid-region, then finish slightly lighter again. Through this mechanical constraint, you end up fatiguing out the whole way through, as opposed to fatiguing just enough to not be able to perform the weaker points, when you'd still be capable of doing the rest. It's pretty clever, and in theory it's fantastic, considering you can't do this too well with free weights.
The problem is that no equipment company actually achieves theory-status on this. Not even the biggest commercial brands. How it's supposed to work, is there's a weight stack and a cord connected to the stack that goes up over a cam, then to your handles, or whatever the thing is that you're actually moving to do the exercise. Varying the resistance all comes down to the shape of the cam. The distance the cord is from the center of the cam determines the amount of resistance. The further from the center it is, the lighter the weight is, and the closer to the center, the heavier it is. The cam will rotate with the cord as you move the weight, so making it an odd shape can theoretically change the cord's relative position to the center of the cam at different positions in the range of motion. Hence, Nautilus equipment is named after the nautilus shell, being as that's what they originally modeled the shape of their cams after. And that kind of worked, but the physics was a bit off, and the angles were bad, and the equipment essentially sucked. That's okay though- they were trying something new. It doesn't have to be perfect the first time. But it would help if it eventually did get better. If they learned something from their mistakes and revised accordingly, good equipment would exist. But they didn't. Now they either have the cam rotate so minimally, that the shape doesn't matter, or it's a perfect circle, so there's no amount of rotation that could change anything.
So on grounds of the Nautilus theory, machines still have absolutely no advantage over free weights. Because of this, you could argue that the free weights have the advantage as far as range of motion, but you can also argue that the range of motion you're working through in good machines (comfortable ones) is what you want anyway. So ultimately, there really isn't a difference between free weights and today's machines. The machines just kind of missed out on being "possibly marginally better."
There is one line of machines of which some could produce better results. Lifefitness makes a digital circuit that controls the eccentric and concentric weights differently. You should know about concentric and eccentric by now. This line of equipment adds weight to the eccentric motion. Because that's where your results come from, and it's hardly possible to do with free weights, these machines have the potential to be more beneficial in generating results. Only about half of them operate through good angles though (the comfort issue again). So if you have access to this line, only use the ones that feel comfortable. The downfall to this equipment is that you probably don't have access to it. They cost about ten grand per machine and very few gyms carry them.
The other possibility of more effective machines, is the eventually-coming equipment that has a high-frequency vibration while you're completing the range of motion. I'm not sure if these are even out yet, and when they are they'll be even more expensive, so you probably won't have access to these either.
So here's your general summary: the future of machines is fairly promising as far as being better than free weights in some motions- not squats. Squats are perfect. There's no replacement for squats. Nor do I see a replacement for some of the other fundamental compound movements. But chest, biceps, triceps, shoulders, and maybe abs and back could be worked more effectively with machines if they're designed right. But not so much right now. Right now free weights and machines are essentially equal aside from a couple of the fundamentals- particularly squats.
So realistically for now, you should use both machines and free weights with no concern for technicalities, just comfort.
I have a Boflex. Where does this fit into the machine/free weight ranks?
Unspeakably lower than the second worst machine ever made. The Boflex is ridiculous. I'm exceedingly sorry that you wasted so much money on such a pile. It would have been better spent on kind of expensive cats with no legs. The potential for results with that purchase is probably vastly greater. The issue is that the Boflex applies force with those metal bands that bend a) not smoothly, such that you're more susceptible to injury, and b) progressively requiring more force. So effectively the optimal variable resistance is virtually entirely backwards. It's harder to pull at your weaker more-contracted state, and easier to pull at your optimal strength point. So on a physiological and mechanical basis, Boflex is the worst thing that's ever happened to exercise.
Additionally, I'm going to tell a sweet, sweet Boflex story... Actually, now that I'm thinking about it, I probably shouldn't out of respect for people's privacy, but I badly want to. Okay, nevermind- I better not. Here's the deal though, if you talk to me, ask me about it. "Hey Courtney, what's the Boflex story?" "Ah... Have I got a story for you!" And then I'll go on. In the mean time, just work out with legitimate equipment until such times as my jovial story graces your supple auditory canals. Pow!