In the last few weeks I've played all three of these, and friends have told me that this one's rubbish, while this one's great, and so on. So I decided to compare them myself.
First things first: all three owe a lot to Call of Duty: Modern Warfare. They all have lashings of American flag-waving, they all follow the modern trend of "realistic" armaments, and they all depict special forces of one kind or another. And two of the three have overblown, apocalyptic plots.
Graphically, the differences are greater than you might expect. While Battlefield boasts destruction of scenery and a strangely pleasing, slightly cartoonishly stylised aesthetic, I don't think anyone could argue that its graphics match up to either of the others. As for destructible terrain, it's a freedom with limitations. Outer walls of buildings can be blown up, and the building will collapse when they're all gone - but the inner walls are, until that point, mysteriously impregnable; wrecked vehicles lie strewn about, but a wrecked bus remains impervious to anything I throw at it; physical properties remain unsimulated, unlike the physically-accurate engineering in, say, Red Faction Guerilla. It doesn't help that all that damage modelling is obscured behind masses of realistic but hugely irritating smoke, dust and mist.
Medal of Honor and Call of Duty: Black Ops both aim for a more photorealistic effect, with varying degrees of success. Medal of Honor has phenomenally beautiful landscapes, but suffers badly close up. The bump maps are overdone, for instance, and there are a number of other small issues, but occasionally bigger issues crop up, everything from major things to small but significant things that knock your sense of immersion. For instance, on the first level I fired a couple of rounds at a pickup truck's lit headlights - and they remained lit. A closer look showed that the headlight showed metal bullet hit decals, rather than glass hits, and the windows proved similarly indestructible. In a big release like this, I expect glass to shatter, lights to get shot out, and hit decals to be the right kind for the material they're on. It's not good enough.
Black Ops doesn't seem to go for any gimmicks or revolutions, just a quick polish of an already solid graphics engine. It feels familiar, with all the advantages and disadvantages that the CoD4 engine brings. It feels stable, runs quickly and smoothly, and and for me at least had the most aesthetically pleasing look of the three. Nothing terribly exciting, but it just does what it should and does it without making me think "Wait, what was that?" Which is all you can ask of it, really.
In the soundscape - and bear in mind I'm largely playing this with the speakers turned down quite low because I don't like disturbing the neighbours, even though they are cattle - there's not a lot between them, though my admittedly dodgy memory says the weapon sounds in Medal of Honor were weedier than in the other two. Battlefield has some very nice sound effects, and may indeed just edge out Black Ops in this instance.
The plot and story are the big thing for me, along with gameplay, and that is where the real differences come in. Medal of Honor is easily the weakest, with really only a short narrative of one operation during the war in Afghanistan. It has no real sense of what's at stake, and apart from a couple of short missions playing as the gunner of an Apache attack helicopter, no moments that really stand out; it's just an endless (can something this short feel endless?) series of "hold this position while millions of Taliban 'insurgents' attack you" missions. Worst, there's no real ending; you just exit a cave, get on a helicopter, and cue credits.
Battlefield and Black Ops both have more elaborate and interesting plots, essentially representing two distinct film genres; Battlefield is the Hollywood summer blockbuster, with big action setpieces, implausible escapes, big explosions and World War 2 flashbacks, while Black Ops is the taut thriller starring Gary Oldman, brainwashing and Vietnam flashbacks. (Oh, and in an interesting connection to another of my interest, revolves around a numbers station. Go on, wiki it.) Both stories are solid and work well, but I preferred the dark tone of Black Ops, not to mention the fact that I actually got to do the interesting stuff in it; in Battlefield, an awful lot of "the cool bits" occur in cut scenes, a method that when you're used to Black Ops' narrative style makes you feel slightly detached from the story. So it's pretty much down to whether you want action or thriller - consider it a choice between Black Hawk Down and Enemy of the State.
Gameplay is, of course, the key. A great story will fail if the gameplay is poor, while even a game with no story will be enjoyable if the gameplay's good enough, and on that front all three have their appeal. Personally I preferred the weapons in Black Ops, though Medal of Honor felt like it handled very slightly better overall (although there were some horridly poor moments, like the laser designator at the airfield). Battlefield has a strange and undeniable feeling of "like BF1942 but with plot", which is unsettling at first but quickly fades, while Black Ops ends up feeling like you're watching and starring in a film. There are niggles, of course. Black Ops, for instance, doesn't tell you that if you have your mouse inverted it won't be inverted when controlling projectiles, and the segment where, as an SR-71 navigator, you control a squad on the ground through a top-down view that feels like a less polished version of a late-nineties strategy game, feels like a substitute that never quite works for CoD4's magnificent "Death From Above" mission. Battlefield has a habit of forgetting the grenade launcher attached to my rifle, and "unarmed" missions go by with soldiers apparently forgetting the pistols quite clearly strapped to their thighs. Medal of Honor... well, Medal of Honor is more niggle than game, and really I'm just incredibly glad EA gave me it at 75% off.
Anyway, the point is that of all of them, I paid full price for Black Ops and don't mind at all. I paid budget price for Battlefield, and given its focus on multiplayer (which I rarely play) £14.99 is just about right for me. And Medal of Honor is a decent game for £9, and I'm bloody glad that's all it cost me.