Turn Based
Strengths - Turn-Based combat provides the player with ample control over their players, with no reliance on player reflexes and allows for many more tactical options and choices to be incorporated into gameplay. It progressed in a measured manner, which allows better planning and anticipation from the player's perspective, but also serves to reinforce the idea of discrete progression through a game, a typical RPG trait that is being adopted across the whole spectrum of gaming genres due to it's effective nature as a player hook. Tracking of enemy actions is much easier in a TB system due to it's sequential nature.
Weaknesses - Poor design becomes glaringly obvious in TB combat. Sprites animating too slowly can drag combat out needlessly, as can viewing of movement that is hidden/irrelevant to the player. However, the biggest downfall of TB systems is providing combat that offers no challenge, as this ends up being a timesink that generally isn't worthwhile to players. Some of the more dubious TB weaknesses include the fact that it isn't trendy, and that it generally requires an attention span of some kind. Finally, TB will always be an abstraction of reality, and as such fails to appeal to a realism obsessed market, even if it provides a more accurate portrayal of reality once all sequential abstractions are rationalised as simultaneous actions.
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Real Time with Pause
Strengths - The addition of pausing to a RT combat system greatly reduces the reliance on any kind of manual dexterity on the players' behalf, and also is less limited by a need to streamline the HMI. Poor design is also more forgivable, due to the simultaneous actions allowing players to get through encounters that offer no challenge at a faster rate, as long as there aren't enforced round times.
Weaknesses - The very philosophy of adding a pause to a RT system is akin to whittling away the corners of a square peg so it fits in a round hole. It addresses the problem of difficulty interfacing in RT, but doesn't get to the root of the problem. In taking away a reliance on player dexterity, a challenge that is vital to RT systems is now gone. In order to effectively compensate for this, there needs to be a challenge in the tactical play, however, that too is compromised by the inability to effectively utilise terrain and cover, or attack while moving, which greatly limits many actions that would commonly take place within a real world tactical simulation. Also the nature of pausing to issue orders and then watching those orders get carried out seems entirely too passive, while on te flipside of the coin, you are constantly pausing which serves to eliminate most of the advantages of a RT system. So basically, taking a real-time system and adding pause comes with all the weaknesses of RT systems, few of the strengths, and is far outweighed by both TB and purely RT systems.