The term "long" is generally used to refer to something that is moving in the same general direction as the underlying, so all calls are long, and all puts are long. I'll assume that by "long", you mean "out of money".
You've likely heard of the mean and variance of a distribution. Those are first and second order parameters, respectively. The mean tells you the expected value, which for a stock should be (apart from risk-discount issues) the stock price. The variance tells you how risky the stock is. The value of a call is basically the expected value of all prices above the strike price, while a put is worth the expected value of the prices below the strike price (this is a simplification, but I think it's close enough for this question).
There's the further parameter of skew, which is a third-order parameter. Basically, this tells you how far from being symmetrical the distribution is. For a symmetrical distribution, the options will of course be equally valuable; the distribution will look the same x above the mean as x below. But if one side has a longer tail, then that can cause them to have different values.
In statistics, skewness is defined as being the expected value of the cube of the $z$-score, E[((x-mu)/sigma)^2]. Larger skewness tends to mean more differences between options with the same difference from market price, but the exact difference isn't completely determined by the skewness, but depends on the distribution.
As an example of a distribution with significant skewness, suppose you roll twelve dice, and get a dollar for each six that comes up. The mean of this is 2, so the "market price" of this game is $2. Now suppose we have a call option with a strike price of $3, and a put of $1. The put is worth money only if you roll no sixes, which happens 11% of the time. So it's worth $0.11. The call, however, is worth money as long as there are more than 3 sixes, and the more sixes there are, the more it is worth. Each individual roll is worth less: the probability of getting 4 sixes is only 8%, 3% for 5, etc. But there are more numbers greater than 3, and each of them is worth more. Overall, the call is worth $0.17.
This is a positive, or right, skew distribution. In a case like this, where a "stock" has really unlikely possibilities, but the payoff for those possibilities is really high, that tends to make calls worth more than puts. Actual stocks with highly positive skewness can often, as in this example, be modeled as being the sum of low probability possibilities. This is a highly simplified model, where each die has the same probabilities and payoffs, and each is independent of the other. While the real world isn't that simple, this gives a general idea of the principles involved.