Which is the best Solution for VMware VDI?

- Is a converged platform from HPE, Dell or Cisco better or is it better to go with the traditional methodology of Blade / Storage infrastructure for a typical setup of around 2000 full VDI desktops?
This would really depend (yeah I know not the best answer in the world). The dependencies are pretty straight forward though i.e.
* Do you have SAN...etc storage in house that you can leverage for this?
* Do you have the technical staff to support a SAN / Storage infra?
* Do you have budget for expansion / on going support cost for a SAN / Storage infra?
We used to run traditional VDI (Blades with either SAN or Netapp NFS) and recently moved to HCI. For us HCI made sense and allowed us to expand, reduce our VDI environment and re-task esx hosts as needed to our Server Virt environment.
There are a few key players in this space (Nutanix, Simplivity ...etc), my suggestion is to do a lot of testing with each of these solutions to see which ones fit your immediate needs and can expand into future needs (i.e. adding GPU's to the esx host )

- Is this the best solution for a large global setup?
This again would depend on how many users in each region and whether all the users in that region connect to the same infrastructure. A common design is 2 data centers in each region where the majority of the users are located and splitting the VDI instances between the 2 data centers (for resilience / DR)

- What are the typical challenges faced in such VDI setups in terms of performance, booting, peaks and failures?
In my experience, testing the most resource intensive actions (i.e. boot storms, patching ..etc) in a proof of concept will surface some issues either with the design, the product(s) that you are using in this design. Performance is a tricky thing as it is very subjective, you might think performance is good, but that 1 second lag with a screen refresh can be seen as a performance issue with the user. While you want to avoid "over engineering" a solution, you really want to get familiar with the target users of the solution, how they leverage it, what the application profile / footprint for those users are so you can tailor it to their expectations.
One of the biggest issues that I have run into In the past is not using VMware's "linked clones" or Citrix MCS. This reduces storage capacity needs and allow master image updates very easily/

- What are the precautions one should take while solutioning such a setup?
Like I mentioned above, you really want to get familiar with the target users of the solution, how they leverage it, what the application profile / footprint for those users are so you can tailor it to their expectations.

- Most of the principal vendors will always push their solutions to be the best but in reality what should the end customer be aware of?
Cost, complexity and being able to support it. If support and complexity of a solution is hard / a lot, your project will fail.

- Are there are any practical rule of thumbs for full VDI, as to how many VDIs will work on a single server?
Again, this really depends. You will hear some astronomical numbers that some vendors come up with, most of which do not apply to any applications that you run in house. Knowing application profile / footprint for those users and how an application works and responds will definitely help determine an estimated capacity for you. Tools like LoginVSI, load runner, ...etc that simulate user activity on a VM or SBC environment will definitely help, although you need to put some time in to develop some custom test scripts based on your application profile. It seems like a lot of work for just capacity estimation, however you can use this as a base line for regression testing of MS Updates, App updates, Configuration changes and even OS Upgrades.