A stand alone splitter gives you more options of where you can use the splitter and is easier to move around when not on the tractor. Both take up about the same amount of storage space.
Stand alone splitters generally have faster cycle times than 3PH style, a lot has to do with your tractors hydraulics. The cycle time of a splitter is an important consideration.
A 20 second cycle time may seem like a pretty quick turn around however, cycle times are figured when the pump is running on the first stage of the hydraulic pump, high volume low pressure. When the pump hits the second stage the pressure increases and the volume goes down which slows down the ram and increases the cycle time.
Using a powered splitter is a lot easier on the body. The price of wood splitters varies greatly. There are some very good splitters to be had at a reasonable price, so are a little more expensive. Depending on the amount of wood you plan to split and the time you have to do the work will dictate on how much you should spend.
Timber Wolf makes a good splitter but they are priced a bit higher than others you might in box stores. I purchased a Super Split 4 years ago, they are one of the more expensive splitters. I split around 12 full cords of wood every year and wanted to save time. With a 4 second cycle time, more like 6 or 8 seconds when the splitting gets tough, I can breeze through a pile of wood in pretty short order.
Really take a close look at what you want from a splitter and how much you are going to use one then look for the splitter that best meets you budget and needs.
Randy