Geldenhuys and Hansen showed that a kind of ω-automata known as Testing Automata (TA) can, in the case of stuttering-insensitive properties, outperform the Büchi automata traditionally used in the automata-theoretic approach to model checking. In previous work, we compared TA against Transition-based Generalized Büchi Automata (TGBA), and concluded that TA were more interesting when counterexamples were expected, otherwise TGBA were more efficient. In this work we introduce a new kind of automata, dubbed Transition-based Generalized Testing Automata (TGTA), that combine ideas from TA and TGBA. Implementation and experimentation of TGTA show that they outperform other approaches in most of the cases.