Why is GTP, not ATP, produced in Gluconeogenesis & TCA Cycle?
Nice question. Beginning with Krebs cycle, there is actually no specific answer as both GTP and ATP are produced. First, see this article for why GTP is the more frequent product:


  It may be that at the beginning, both GTP and ATP were equally available for energy and that the succinyl CoA synthetase reaction happened to choose GTP and that reaction is still with us today, billions of years later, even though we run the TCA cycle clockwise (forward) instead of backwards.


So, actually both ATP and GTP can be produced. And indeed both are produced, depending upon the organism. See this article:


  A step with significant variability is the conversion of succinyl-CoA to succinate. Most organisms utilize EC 6.2.1.5, succinate–CoA ligase (ADP-forming) (despite its name, the enzyme operates in the pathway in the direction of ATP formation). In mammals a GTP-forming enzyme, succinate–CoA ligase (GDP-forming) (EC 6.2.1.4) also operates. The level of utilization of each isoform is tissue dependent. In some acetate-producing bacteria, such as Acetobacter aceti, an entirely different enzyme catalyzes this conversion – EC 2.8.3.18, succinyl-CoA:acetate CoA-transferase. This specialized enzyme links the TCA cycle with acetate metabolism in these organisms. Some bacteria, such as Helicobacter pylori, employ yet another enzyme for this conversion – succinyl-CoA:acetoacetate CoA-transferase (EC 2.8.3.5).


So, there is no strict rule that only GTP will be produced instead of ATP at that step. And, afterall, it does not matter much as both of them carry equal energy.



Now coming to Gluconeogenesis, GTP is hydrolyzed by the enzyme Phosphoenolpyruvate Carboxykinase or PEPCK. This enzyme can also work with both ATP and GTP, depending on the sepcific type of enzyme. See this article (links added separately):


  It is classified under EC number 4.1.1. There are three main types, distinguished by the source of the energy to drive the reaction:
  
  
  4.1.1.32 - GTP (PCK1, PCK2)
  4.1.1.38 - diphosphate
  4.1.1.49 - ATP
  




Thus, there is no strict protocol for using specific energy carrier in the process, both ATP and GTP can be used in the reaction. Its just because GTP is more frequently used that it is mentioned instead of GTP/ATP in the reaction.