Vermeer and Morbark provide information on these two processing methods.
Tub grinders generally perform better with larger and heavier material such as stumps and large roots. If the material is consistently longer in length, then a horizontal grinder is better suited. Tub grinders generally have higher production rates so are better suited to situations where there is lots of material to process. However, if the material is longer and quite bushy, then a horizontal grinder could operate more efficiently. This is due to the limited depth of the tub of the tub grinder, which makes it more difficult to feed longer material. If working with longer and bushy material, then another advantage of using a horizontal grinder is that the material does not need to be cut into shorter lengths, with a chainsaw for example, as would be necessary with a tub grinder.
Tub grinders need to be operated in more remote locations, as material can fly out of the tub and pose a safety risk. If this is not possible and the grinder must work in more confined spaces, then the horizontal grinder should be used. It is much better at containing material within the machine.
Smaller loading equipment can be used with horizontal grinders as they have a lower feeding height than tub grinders. Tub grinders sometimes have the option of an integral loader. The cab of these units offers the operator good visibility into the tub for optimal loading. Horizontal grinders can often have the option of being track mounted or are towed. Tracks give the flexibility of being able to move around the work site on its own. Tub grinders are also easier to work on and maintain. Source: http://www.morbark.com and www2.vermeer.com