For sake of covering all my bases, I'll begin with brief, simple definitions (that I'm sure you probably know, but can't say for others). Much of the material is heavily paraphrased or explained in references listed.
Positive reinforcement is the process by which certain consequences of a response increase the probability that the response will recur. (Let's stick with primary to simplify things a bit.)
Negative reinforcement is a process by which a response that leads to the removal of an aversive event is increased.
NOTE: Punishment is not an equivalent nor interchangeable term. Punishment is an aversive stimulus that is presented specifically to weaken or suppress an undesired response.
There have been studies on the effectiveness of various permutations of stimuli and forms of reinforcement. Continuous reinforcement is when every response is reinforced; this is powerfully effective in rapidly achieving manipulation of behavior - though these changes are easily reverted if suddenly reinforcement is suddenly lifted.
In contrast, partial, or intermittent reinforcement has been shown to be a means to continue/keep behavior... resistant to extinction. A classic example is that with casino gambling - one's reward is obtained at various intervals of time. The first and occasional introductory "wins" may provide feelings of exaltation. In addition, since gambling requires a cost in order to continue with the behavior, the well-known gambler's fallacy, a game-theoretic/ecomomic dilemma concept that may also be at play.
On the other hand, punishment deals with the intent to reduce the probability a certain response will reoccur. Deals with the intent of causing undesired consequences the subject will attribute to a given behavior. "In learning theory the punishing event delivered is always contingent on performance and demonstrably reduces the frequency of the behavior being punished." ^1
There are examples of various 'reinforcement schedules' ('algorithms', statistical patterns, heuristics, dependent on the objective); if positive stimuli or reward and negative/neutral results manifest fixed-ratio; simply put, the subject of conditioning will catch on, whether the ratios are "behavior" or "time-interval" contingent. The subject will catch on to the pattern, consistency, and this influences the strength of the conditioning effort. Conditioning tends to be most successful when the reward if given on occasion, with time-dependent variability between isolated events.
The most effective strategy generally is to follow with how the use of slot machines manage to get people addicted. "Response rate does not change between (?) reinforcements." The time-variable (desirability irrelevant) chance for reward, spin-to-spin, has been shown to be the most effective.
You may find Premack's Principle relevant to your questions. This concept states that a behavior engaged in this high frequency (intensity) can be used, intentionally or not, to enforce low-frequency.
I have a couple other sources I need to skim through to fix up my response make any statements made more affirmatively concluded from well-designed experiments.