Update
OK, I've continued to use these two Prostaff Surge racquets, one strung with the TNT fat core and the one strung with the NXT max. After my experience with the close loss to the pusher I inspected both racquets. Nothing obvisously wrong with the string jobs. The bad experience with the fat core must be that it is not a good string to play when playing against someone who puts no pace on the ball. Too difficult a string to use when you have to supply all the pace on the ball. Whereas the NXT max is a softer, more elastic string with more feel and grip on the ball. I was able to use this string against the pusher more effectively.
I next used the two racquets in a doubles match against opponents who put some pace on the ball. The TNT fat core was a much better string in that game, especially at the net, where it allowed me to hit my volleys deep and with pace more easily than did the NXT max.
I then used the two racquets in a singles match against an opponent who produced moderate pace. The TNT fat core allowed me to hit some screaming forehand winning service returns, and generally provided me with more pace on my own serves.
However, I lost both the doubles match and the following singles match, so neither string was enough to compensate for my inferior play relative to my opponents.
A continuing caveat with this comparison of these strings is that the TNT fat core is the far fresher string job. The NXT max has been in my racquet for a far longer time. A better comparison would be if I had each racquet strung fresh with each string.
But obvisously the most important point for me is to improve my game. Neither string will help me much if I don't do that.