Depends on your infrastructure,
I currently work with a Towable airstart but have had experience with a number of self propelled ASU's (air starter unit).
Depending on the airport, the tow-able unit will work out cheaper as the unit will not require an airport tax depending on your location, however is annoying to park up next to a 747 whilst the jet bridge is connected and the loading staff are still working on the front on the opposite side, which leads to the staff having to reverse in a narrow gap or wait until the aircraft has been fully loaded and potentially delay the aircraft. (A quick fix was to lengthen the hoses)
A tow-able ASU can be heavy and requires a fair sized tug to pull the ASU's around so we usually use a diesel tug specially for this, but that doesn't mean electric tugs cannot pull it. (In our case the tow eye is too big to fit onto our electric tug's latch which pre-dated the ASU)
The problems I find with any tow-able stock is that you have to find the "tow'er/tug" before you can get the kit to the aircraft, and depending on your airport, it could be in another terminal.
Drivable is great but it depends on the usage!
Pending you do a risk assessment and speak to the manufacturer, all tow-able equipment should reach health and safety standards, but its very hit or miss with ASU specifically as you can get really quite ones that just do airstarts and not aircon, some that are deafening that do both and finally you have the bottle air-starts that need to be recharged after every use.
Ramp staff if they had the choice would go for self propelled equipment every day! but being in the ideal world, air-start units are hardly used in comparison to other equipment so you have to look at the customers you handle and what their aircraft are like and if your ASU will be used much.
Some airports can be very small and parking is a big issue, so if you do have a towable unit please look at finding a drive in and out space to ease the ramp staff's time (all they want to do is grab a cup of tea!?)
Further into your question we also operate tow-able steps which will be required by the health and safety executive (UK) to be removed from the airport or electric motors to be installed to aid the operator, as this is one of the main causes for manual handling injuries other than bags.
Tow-able belts are again a cheap option but not ideal in a large airport or being used on larger aircraft as your staff will be constantly towing equipment to the stand, with a limited amount of tugs.
Tow-able pallet dollies can have their advantages but again depends on the infrastructure at your airport and if other handlers use lorries to gain access to the pallets.