Musk has said that the capsule was designed to land anywhere in the solar system. As doubtful as that sound, I can't think of any reasons preventing them from landing on the Moon.
Wouldn't it make more sense to test the capsule by landing it on the Moon (no travel time, no need to wait for transit window, etc.) instead of Mars? Is there any fundamental difference between the two that would prevent flying essentially the same spacecraft to both?
No, not really. SpaceX has been focused on Mars for a long time. It would gain nothing by landing on the Moon towards that objective. The only advantage as compared to Mars is the timeline is considerably less, taking only a few days vs a few months. The hardest piece isn't landing on an object, it's landing it in the thin atmosphere of Mars. Bottom line is, SpaceX wants to land it on Mars because that is their goal.
For a mission to Mars test should be done in Mars and for a Moon mission test should be done at Moon, because we have here different situation. Concentration for manned space exploration now is to Mars, for something new not achieved yet, so the interest it is more for that destination. In this way to fulfill their purposes and what they want to achieve with their Red Dragon, tests should be done to Mars.
As per info in Wikipedia you can find for Dragon V2 that according to Musk launching the Dragon spacecraft with Falcon Heavy could transport to Mars 2-4 tons payload and has capability even for a mission to Europa. For beyond LEO missions I guess probably they will do upgrades. But to be sure that for different missions beyond LEO we will have different configurations. For destinations with atmosphere as Mars it would have a heat shield and parachutes, for destinations without atmosphere as Moon in place of the heat shield and parachutes system mass, it would have more propellant available to descent and approach to surface slowly and touchdown safely.
Moon landings test would not help too much because Mars landings are different case with different condition. There is atmosphere, different gravity and orbital speeds. So in this way we have different procedures and spacecraft configuration. Landing on the Moon it would be just to spend time and moneys for something proved before because they will not get useful data and information for Mars landings. In other words “calculations” are different because we have different situation.
Something else that I want to write about the Mars landing attempt it has to do with reasons that SpaceX is focusing to Mars and concentrating energies to this missions. This reasons make another difference between Moon and Mars mission.
So let see the situation for a Moon landing and a Mars landing. For the first one we are speaking to prove a technology already done so it hasn’t too much interest. It will look like landing for show since the focus in space exploration as I said above is for something new, different, not done yet as landing a human-rated spacecraft to Mars. Landing for show are trying some companies for the Google Lunar X Prize, putting a Lander with a rover in the surface of the Moon. For the SpaceX in the future for commercial reasons could be as an option for tourists to make landings in the Moon or maybe for Moon bases and laboratories. But this is not so near, a lot of tests should be done to make perfectly safety with 100% success for manned missions and for this tests a lot of money must be spent by SpaceX himself, alone without any help, because for this NASA would not fund since is focused to prove Mars landings and doing improvements for success there. Also for a supposed tourist option, SpaceX needs to do new developments. So in these types of Moon missions, it should make possible not just to land but even to get back home safely. In the Mars case it is important for now, just to prove landing a human-rated spacecraft or Lander, safely which has interest. Remember that NASA is trying with flying saucer which is partial successful and without warranty that could work. SpaceX has proved to land something heavy ( Falcon 9 first stage) and knows how to deal with gravity to land softly heavy vehicle. The very useful data taken in this landings are very important for a place with more gravity than Moon and with atmosphere, the Mars. SpaceX is proving capabilities for a Mars landing, or at least they are almost at the finish line and trying to prove it by testing as fast as they can in the first mission of Dragon spacecraft beyond LEO.
This would give SpaceX the chance being part in one of the biggest manned space exploration projects and it would have the most important role, landing a manned spacecraft safely, making it a key element. Interest for Mars it is even for NASA even for SpaceX. Also NASA would be interested for SpaceX which achieves success even with low cost, so for a program to Mars would be better even for NASA. Although Musk has shown ambition to have their own big Mars rockets (Interplanetary Transport System project), their own Mars missions and colonizing it, would agree a collaboration with NASA which has interest and can fund it. All the private companies would like this. Remember in the Moon program in 60s, private companies were in race with each other in competitions to win the contracts and the patent for a technology, without even knowing too much for space because of course it was the beginning of the space age. And they offered themselves with their projects to receive one part of the budged for the development of new technologies for example a human-rated Lunar Lander, without knowing too much for space. SpaceX already have the capabilities to achieve a Mars landing of the human-rated spacecraft. It is ahead and gone even further than NASA has done for this part.
So firstly choosing Moon landings would not give the useful data needed for Mars landing since between them are different conditions, and also SpaceX would be more interested to have collaboration with NASA for a Mars program, staying at the first places for private companies because of their achievements.
From LEO to a lunar soft landing takes about 6 km/s.
Unlike a moon lander, a Mars lander can use aerobraking to shed velocity on arrival. I'm not sure how much aerobraking the Red Dragon would do but I'd venture to guess delta V from LEO to soft Mars landing is around 4 km/s.
