Would the Concorde have been better off using a tailed delta wing?
The beauty of the pure delta configuration was you could get a reasonably low supersonic drag configuration in a planform with a lot of wing area, essential for really high altitude cruise and for reasonable landing speeds without high lift devices.  It was a good overall compromise for Concorde's mission.  

The Avro Arrow, produced then scrapped in Canada in the late 50s, also used a large pure delta plan form (which is thought to have had some influence on Concorde, a lot of Avro's engineers having joined the Concorde program when Avro Canada vanished).  This allowed it to meet the RCAF's specification that required M2+ while being capable of sustaining a 2G turn at 50,000 feet, something no interceptor could do at the time.