This depends on what volume and type and of wood you are intending to split and what your needs are. The following simple guidelines should help.
Horizontal Log Splitters
These tend to sit on the ground and are suitable for most households, with the ability to handling a reasonable range of log sizes. Horizontal log splitters tend to be compact and generally exert between 4 and 6 tons of pressure. They are perfect for home fires and a limited number of domestic wood burners. Some of the more sophisticated horizontal log splitters have stands or legs, which enable you to work at waist height to reduce the potential for back-strain. Some come with transport wheels for flexibility and storage purposes. Horizontal Log Splitters, almost without exception, are mains electricity powered.
Vertical Log Splitters
As the name suggests, these machines work upright, with the wedge moving down into the log. They are therefore a little easier to use and are designed for a wider range of log sizes. Vertical log splitters will have a base plate on which the logs rest. This is usually adjustable horizontally to accommodate the varying lengths of log. This means you can work faster without wasting any time and energy since the hydraulic ram or wedge will often be moving shorter distances. Vertical machines are generally fitted with transport wheels for flexibility, enabling you to work in different areas. Vertical Log Splitters can be mains electricity or petrol powered.
Tow-Behind Log Splitters
Tow-behind log splitters are usually petrol machines, and are usually towards the more powerful end of the market. They can have splitting pressure of up to 25 tons or more and will tackle heavier, knotty woods and tough grains. Most tow-behind log splitters can be used can be used both horizontally and vertically and can be towed behind a variety of vehicles. Some have a ball hitch for use with by SUVs and some are fitted with a pin-hitch for towing behind lawn tractors and some ATVs.* Tow-Behind Log Splitters are nearly always petrol powered.
N.B. It is worth noting that most are not road worthy and are more appropriate for use on large private grounds, private roads and so on.