What is the difference
A "high cycle" battery is referred to as an SLI battery:
Start
Lights
Ignition and is commonly a car battery and its job is to provide a large amount of current over a short period of time.
This large, quick burst of current is used to crank the engine over when starting up. When the engine starts, the alternator usually provides all the power that the car requires, therefore theoretically, the car battery should be able to last its entire life without ever being discharged more than 25 percent of its total capacity. An SLI battery has a greater number of plates internally and are thinner than those found in a "deep cycle" battery. It uses thinner and more plates in order to increase its
surface area thus being able to deliver a large amount of current in a short period of time.
Note:Surface area is the amount of available plates submerged in the electrolyte inside the battery. The more plates you can pack inside the battery, the greater the surface area in contact with the electrolyte, the greater the amount of current released when required. This has a trade-off though. The thinner the plates, the quicker the damage occurs through deep discharge. Plates can buckle, rust etc.
The "deep cycle" battery's job is to give you a steady amount of current over a prolonged period. This battery also gives a surge when needed to start a car, but not as high-powered as a car battery can. A deep cycle battery is so designed that it is able to be deeply discharged many times over whereas an SLI battery will be trashed fairly quickly by repeated deep discharging. Thicker plates are used in the construction of a deep cycle battery so it stands to reason that if less surface area is in contact with the electrolyte inside the battery, less instant, high power is available. In other words, the deep cycle battery has less instant energy but provides greater long-term energy delivery.
Which is best and thus recommended
Dunno........depends what you want to use it for
Recommended applications
SLI: Exactly what is says, Start, Lights, Ignition
Deep Cycle: Boats, Marine applications, Recreational Vehicle (motorhomes) Camping
Bear in mind what I've said here is but just barely scratching the surface. The make-up and composition of a battery is a subject that can span many pages when trying to explain it.
Hope this helps you a bit