I think that the vertical mills are better than conventional ball mills because they have a good pneumatic classification. And other better characteristic is its flexibility for change between different clays.

A VRM is more energy efficient than a ball mill. It consumes less electricity. The VRM takes up less space in the milling complex than a ball mill.VRM is a sure choice of the modern day milling in an energy depleted world.

I think the original question does not refer to wet or dry milling, so we have wet vertical ball mills and wet horizontal ball mills and dry vertical ball mills and dry horizontal ball mills.

Even Balls is a general term , cylpeps , steel balls , beads etc. are used in ball mills and some mills which use balls are not called ball mills

The metallurgical dictionary can be confusing! So what type of milling are we talking about?
We manufacture and market high intensity vertical wet bead mills called a Commett Mill which principle parts can be installed in a Deswik mill and dry autogenous micropulva mills ( no balls ) http://is.gd/ybiAKy 

Original theme is “what are the advantages of vertical milling machine compared to conventional ball mill?" Please be free to elaborate on the equipment you manufacture even if we divert a little.

To summaries

Large rocks are effectively broken by crushing/compression.
Fine material by impact grinding/cataracting
Ultra fine grinding / attrition are effective on for production of -75 micron down to 2 micron product.

As I see, nobody consider the capacities for vertical mills during operation. Basically, vertical mills in different models have less capacity than ball mills. As I know, just in cement raw material grinding, vertical roller mills have been developed.

IIT has patented new vertical milling technology that combines low energy input with maximum grinding force to accurately control the specification of fine powder output. Throughput capacities can also be controlled by both the size of the grinding chamber and a modular approach that enables multiple grinding systems to be incorporated in special twin mill configurations. The system is now being taken up in a range of material and mineral processing operations.

I see that several have answered based on dry grinding, i.e. Vertical Roller Mill vs. conventional Ball Mill. If we instead focus on wet grinding, we should differentiate between stirred media grinding, which can be both vertical and horizontal, and tumbling mills with manufactured grinding bodies. A continuous grate-discharge tumbling mill with grinding balls does seldom have ball size below 20 mm since you then will have unacceptable media losses or problem with grate throughput. To get energy efficient grinding below approx. 40 µm you need to have finer grinding balls than are suitable for the tumbling mill. So, the case for the stirred media mill that often has media in the range 5-10 mm if used as a tertiary grinding step or for re-grinding.

Generally, the VMs are successfully used for very fine grinding. This equipment is very advantageous in comparison with BMs. During the last 3 years, I replaced the BMs with VMs for two magnetite projects. FYI, the power consumption!

I think it is horses for courses - it may not be realistic to replace a wet horizontal ball mill with a wet vertical mill (stirred), but rather have both in the same plant to achieve your ultimate particle size (i.e. wet grind, separate / classify then onto the next stage of fine or ultrafine grinding). Similarly, in dry grinding, the vertical roller mill with integral classifier has a specific task to do. You can also have a horizontal ball mill with air classifying capability. Each machine has a specific role and each plant / process has specific requirements. Yes there are overlaps, but this is where the analysis and evaluation comes in - can we replace one piece of equipment with another, what are the trade off's and benefits?

Maximal feed size accepted by VMs is 6 mm. You can judge if their use is adequate to the comminution circuit in function of the process requirements (product final size, production capacity etc.). Certainly, the VMs are characterized by lower power and grinding media consumption than BMs. Even the CAPEX can be lower, depending of the production capacity. The maintenance costs are lower too in comparison with BMs.

It would be difficult to provide an accurate answer without a reference point as a base to compare the two types of comminution equipment you mentioned. That reference point would have to be throughput rate and target grind size.

It seems from the above that each application will be specific and will require a specific analysis. Vertical roller mills can have lower power than ball mills in most applications for dry grinding. One comment that I did not see here is the potential for differential grinding, especially in vertical mills, but also in ball mills. That is when inter-grinding different materials, the softer materials tend to be ground finer. In air swept vertical mills, this can leave a higher quantity of the harder to grind material in the mill. If this material is also abrasive, it may accelerate wear inside the mill. Which leads to an additional comment vertical mill tend to be more complex and have a higher level of maintenance expertise required? Wear rates (measured in metal loss) tend to be less, but replacement parts are more expensive. This is not to endorse ball mills, which appear to becoming a dying breed. Just to note some more of the differences.

Just add small comments to the previous, you will not need classification equipment such as vibrating screen or hydrocyclone for Isa Mill or Verti-Mill circuit. A signature plot test work to determine the energy requirement per ton of feed, the media consumption of the specific feed is recommended.