It very much depends in which areas you are comparing them. The British Army (naturally) is unmatched out of the the three services when it comes to old fashioned soldiering; engaging in close quarters combat and firefights on the ground, taking enemy positions, etc. While the Royal Marine Commandos excel equally in this area, one must remember that the British Army has assets available to it (the Royal Armoured Regiment, the Royal Artillery) that greatly increase it's combat effectiveness. In this regard, the Army is top dog by virtue of it being, well, an army. The RAF maintains a form of infantry in the guise of the RAF Regiment. This unit is not as many would have you believe on par with Line infantry, the Parachute Regiment and the Royal Marines. While there is no doubt that they are a well-trained unit of men (members of their II Parachute Squadron serving with the Special Forces Support Group), their effectiveness is not up to the standard of an infantryman or marine as they lack combat experience. The RAF Regiment is commonly deployed in airbase defence and merely mount short range patrols around the area. This makes it unlikely that they will encounter the sort of prolonged engagements that infantry and marines regularly deal with.
Of course, the Royal Navy excels at maritime operations, being among other things, a blue water navy. The Navy's fleet of warships and support ships are often at the front of humanitarian aid operations and provide an important logistical element in the Armed forces. There is, after all, only so much that aircraft can carry and they require a landing strip. For example, without the aid of the Royal Navy, it is highly unlikely that British forces would have been unable to retake the Falklands in 1982. In addition, the Royal Navy engages and eliminates the navies and submarine capabilities of opposing nations which is vital in denying the enemy use of ship launched ballistic missiles and naval air power. Without the Royal Navy, the British Army would not be able to operate at the same level it does today, and likewise the Royal Navy would be unable to mount land based operations without the British Army.
I will touch on Chris Ballard's idea that the Royal Air Force is the best service briefly as well. This is a rather ludicrous statement to make (sorry, I don't mean to offend), as if one service was the best, there would be no need for the others. While it is generally agreed within the forces than the RAF have access to the best facilities and accomodation the majority of the time, this does not necessarily make them the best. After all, the Fleet Air Arm matches the RAF's air power, and the standard infantryman of the British Army surpasses the RAF Regiment (let alone if you bring the Parachute Regiment into the equation). Secondly, as shown in Libya recently, despite the RAF removing around 30-40% of Libyan ground forces, they are unable to make any headway as there is only so much that be accomplished from the air; bombs do not discriminate and "eyes on the ground" are often was is required to make decisions at a tactical level.
Finally, let us not even begin to compare Special Forces. 22 SAS and the SBS are trained to near enough exactly the same standard and are currently carrying out much the same missions, often in the same unit.
I hope this has helped you, and anyone who reads it.