I guess the answer is...it depends. Aircraft type, type of fault, runway conditions, weight, etc. Pilot judgement is important. The good news is that there shouldn't be any in-flight controllability issues as there can be with an engine problem so the go-around should be straight forward after which one should have time for a better analysis. On the other hand, a simple loss of autobrake capability should be easily dealt with in most cases with manual braking and a decision to continue with the landing.
Still , there could be unknown underlying issues so why not be conservative in your approach. If the runway is long, for your operation, then things will probably be OK but if it is not, then going around and thinking through the problem may be best. I find the final approach segment to be very busy with crew calls and ATC calls among other things creating plenty of distraction. At minimum, don't accept a long landing(even if within the touchdown zone) when one can simply go-around and try again...just in case there are further issues.
In this incident, the flight crew had a simple autobrake fault message and decided to continue. But the runway was relatively short at just under 7000' with a high density altitude. They landed fairly long and possibly faster than desired and after encountering further issues, ran out of runway. Unfortunately, the link to the official report is no longer valid.
In the second incident, the fault happened in the flare. Should you go around? To be decided by the PIC but who wants to discover that you only have one brake. You might need that brake...to slow down or for directional control depending on the conditions.
"C-GKEW, a Cessna 560 aircraft operated by Keewatin Air LP., was conducting flight KEW501 from
Iqualuit (CYFB), NU to Winnipeg/James Armstrong Richardson Intl. (CYWG), MB. During the flare
for landing on Runway 31 at CYWG, the "power brake low pressure" and "anti-skid inop" warning
annunciators illuminated. The landing was conducted without further incident and the crew brought
the aircraft to a stop on the runway prior to Taxiway A. The crew taxied the aircraft onto Taxiway A
using only the right brake. The aircraft was towed to the operator's hangar.
The operator's maintenance inspection revealed that the left hand brake line had ruptured."