The majority of forklifts sold in the UK are rider operated counterbalanced. These account for over two thirds of all forklift sales in the UK.
Usually counterbalanced forklift trucks are used outside and reach trucks are used inside but this is not the end of the story.
Conversely, reach trucks should normally be used inside but can be used outside in certain circumstances. There is an urban myth that says that reach trucks should be used indoors only. This is not the case but the problem is that the wheels in the reach legs have polyurethane tyres fitted as rubber won't stand the loading.
These type of tyres don't have any "give" in them and if the floor surfaces are not reasonably flat the operator will have a very uncomfortable ride and there is a possibility that the truck will overturn with potentially serious consequences.
Reach trucks can, of course, work in much smaller aisleways than counterbalanced trucks can but care needs to be taken when working out the truck's ability to make a ninety degree turn in an aisleway safely. There is a formula that is used to calculate this and this is described in detail on this page.
There are many other specialist forklift trucks on the market such as order pickers and turret trucks which, by their very nature, are usually specified as part of an overall warehouse scheme and should be perfect for the application. For this reason I haven't covered them here.