The reason for preferring an ASA (or something) over the windows firewall is extremely unclear in this case.
The appropriate thing to do is to assess whether there is any reason that data should not flow from the node on one side of the (crossover) cable to the node on the other.
The answer is a continuum somewhere between two extremes:
- Neither computer is internet-connected and both are used by the same people for the same purpose, and they are equally trusted. A firewall of any kind is likely wasted effort in this case.
- One computer is a publicly accessible node in a DMZ, and another one is connected to a network which processes privileged information. In this case, a firewall is strongly recommended, if the connection must be made at all.
Not knowing where you lie on this continuum makes it very difficult to give a decent answer, but thinking about that might help you arrive at one. It is clear that you lie somewhere in the middle, but you should figure out what it is you want to isolate between the two networks and why it is that they are separate. "I want to isolate connections" is usually not an adequate answer to that question.
As to why one might prefer one type of firewall over another, the best reasons are the existence of a central configuration management infrastructure (or a focus in business expertise) and the need for a particular feature available in one but not the other. Lacking such a reason (and one probably exists), the direction you are being given is likely misguided.
It would be absurd for a public standard to mandate or prohibit the use of certain firewalls by brand name. However, internal standards and contractual standards might well specify such a thing.
The concerns in this case are likely more business than technical.