It isn't too difficult to mod your own spears, bows & arrows if you would like to make them the way you want them. But this would only affect the ones you use unless you gave them to companions or dropped them for your enemies to pick up.
I'm of the opinion that it's a toss-up because the much higher velocity of an arrow gives it deeper penetration (generally speaking, not always). Kinetic energy increases with the square of velocity, so when the velocity gets high it will overtake the mass and give greater overall energy. No, I'm not going to get into any calculations to prove anything because I don't have a problem with this in the game. Just food for thought.
While I agree with the conclusion that you arrived at the end which is that they both would be quite lethal and the difference isn't going to be big, I have to stress again that the idea the kinetic energy is representative of something's ability to damage is a very widespread misconception. The idea the damage is somehow proportional to the square of the velocity and linearly with mass doesn't really hold much candle. The purpose of it is to calculate work/energy-transfer between two objects in a purely mathematical way, and it's not for the purpose of calculating the amount of damage a projectile does.
If we assume that by damage, we mean how lethal/incapacitating a projectile is, let's take make an edge case. Imagine an extremely thin needle, so thin you can barely see it that weighs only 0.01 gram, but it is moving extraordinarily fast, a zipping 30000 m/s. It would have a kinetic energy of 4500 joules, which would be significantly above any arrow or javelin or even most bullets (9mm is about 500 joules, 5.56 from a M16 is about 2000 joules.) However, in reality, this 4500 joules super thin needle actually would do almost no damage to a human's body because it's way too thin and way too fast to do anything more than make a teeny tiny hole in the victim's body. Never mind a 9mm or 5.56, it wouldn't even do close to as much damage as an arrow with 30 joules energy which only has 1/150 of the needle's energy.
If we take another edge case, a massive 5000 kg wooden block moving at 0.1 m/s, again, you have a kinetic energy of 2500 joules, but it's moving so slowly it would just push the victim very very slowly, doing absolutely no damage.
The point is, again, to somehow quantify damage of a projectile, you have to get into deformation mechanics, injury biomechanics and a variety of very very complicated physics and medical subjects. The idea that kinetic energy is anything more than an EXTREMELY rough estimation is very doubtful.
But yes, the conclusion I arrive at is same as yours, I don't see any reason to believe why a javelin would be more lethal than an arrow. As long as you perforate a major organ with a large enough hole so that it doesn't function anymore the victim will be incapacitated/die.