For data center HVAC system which is the best solution Dual cooling system or Dx units?

Dual cooling system and depends upon the size of data center.

It must be Dx units or direct expansion unit for better results. 

Well I believe Dual cooling system is better as it is part of Tier-3/4 type of data center with less downtime. although the calculation is totally depending upon the size of datacenter. 

DX system is good w.r.t. Power Usage Effectiveness (PUE) however, for a Data center, it is better to use Dual System to have an alternate system ready for odd times.

Best is Dual cooling system as chilled water can be primarily used which is more energy efficient and DX can support in case of common fault or power outage. 

Dual Cooling system is highly recommended - Reason : Data Centers are too sensitive that a failure in the temperature maintaining system would shut down the Racks which leads to a huge data & revenue loss.

Dx Units are Recommended in low distance piping run areas - To be honest Now a days there are DX units with Dual Cooling added to it. I have Installed around 8 Units in 1 of my previous data center project.

It is recommended to have dual system.

DX system is best solution.

I recommend to used dual cooling system to ensure and maintain the proper required cooling system & temperature either chilled water system or Dx system. In case of breakdown failure there will be alternative backup & continuous operation.

For data center HVAC system , the dual cooling system is the best choice.

It is called CRAC units : Computer room air conditioning units.

Where there are two cooling coil inside the unit, one using chilled water system (normal operation) and the other is using refrigerant (dx system for emergency case).

in case of emergency the unit will be connected two the emergency power (generators, UPS,.......)

chilled water operated CRAC UNITS since your talking about data centers you will have to surely install thermal storage tank in case of power outrage .so chilled water is recommended.