When it comes to spears, there are a lot of factors to consider. We see both in art, of course, but according to an article by Connolly, the ratio of overhand:underhand is something like 7:3. And certainly there are advantages to both. But if we can only use one animation for your standard spear, then the overhand is undoubtedly better.
http://imgur.com/fSJbwSD
1. Overhand can be used in a tight formation. Here is a fantastic vase painting which highlights what can go wrong with an underhanded grip. But the overhand allows the back of the spear to go over the head of the row behind you without injuring anyone.
http://imgur.com/GbtQUMg
2. There are – I think – two articles that use force plates to measure the energy behind the overhand, underhand, and underhand/high-elbow. The overhand is the fastest and most powerful with the best economy of movement of the arm. The high-elbow hold being a distant third in power and speed. The high-elbow is also a very uncomfortable grip to maintain. I have an image capture of the Connolly chart, but the article itself is expensive so I'm going off what I found at the RAT fora.
3. Shields are very big. The aspis is actually huge and you don't get a good idea of its size until you see one in real life. The same goes for a thureos. Using a spear overhand means you can cover yourself with your shield and strike over it, to the sides, or even down at someone's feet by simply dropping your arm. To use an underhanded grip and to get a good extension of your arm, you have to displace your shield to the left or swing it open (as depicted in art), which means you expose at least your shoulder if not most of your body when you attack.
4. I own the parts for a spear. The pole alone is 7 feet and when I get it tapered I'll be able to attach the head piece and butt piece. It will be weighted so that the balance of the spear is a little back from the center, but not by much. Weapons need to be an optimal weight to be used well: for example most swords don't weigh more than 1 kg and usually less. You can shift the center of balance by increasing the weight of the butt spike, but you get a diminishing return with increased weight of the whole weapon. Balance is exceedingly important for a good weapon and its effective use. Without it, you spend more energy fighting the weapon than you do the opponent.
5. Using a spear underhand and holding it further back doesn't really help. You lose that point of balance. It becomes very easy for an opponent to just move your spear out of line. Recovering is very difficult. Think leverage and points of control. You have more reach, but you're not effective with it.
6. I really, really hate Lindybeige.
7. Overhand never really went away. The Bayeux tapestry shows the grip being used well beyond our time frame.
8. Your opponent probably also has a shield, which means a lot of him is covered. Unless you can get to his side, the only vulnerable parts are his face and behind the shield. You need to be able to reach over his shield to strike at the face or neck with your spear, which you simply cannot do effectively with an underhand grip.
Because of the above, I would argue that even levy troops with minimal training would tend toward using an overhand grip. Imagine the first day of your incredibly short training: Keep your shield up and in front of you and strike with your spear above the shield. Don't move the shield away from you or your dead.
Cavalry is a different matter, but if a cavalryman is using a normal length spear of about 7 to 8 feet, he would probably use an overhand grip.
1. Balance is still an issue. Because of this, the spear is unlikely to extend much beyond the horse being ridden. These aren't going to be shock cavalry. The spear is a primary weapon and you run into the same issues as infantry. If your opponent has a shield, you want to reach over it regardless of whether they are mounted or on foot. A downward strikes against infantry would be particularly effective in this case and easy to do. An underhand would mean contorting your arm. Also, the average horse of the day wasn't very many hands high, so you wouldn't be riding that much above the shield of an infantryman.
2. The development of the kontos and xyston change things by allowing a couched grip so that a charge could be made. But those aren't really close-in weapons to be used after a charge. So totally different game here despite their similarity.
So to conclude, our evidence is limited pictorially, but leans toward overhand. Based on the argument I made above, when it comes to choosing between one or the other I would stick with an overhand grip.