One thing that I think I mentioned briefly regarding Super Robot Wars: Original Generation 2 is that I am on my second playthrough of the game. I am not sure if I actually mentioned that the fact I am going through on a second playthrough has given me a number of advantages. Such a thing is not uncommon at all in RPGs these days, having continuously become more widespread since Chrono Trigger popularized the idea near the end of the SNES era. I am a big fan of Chrono Trigger's New Game+ mode, but in many ways I find different takes on the idea, such as the one in SRW:OG2, to be even more interesting.
Fundamentally, New Game+ modes, game modes that allow you to carry some benefit through subsequent playthroughs of a game, are based on the idea of improving the replay value of the game. There are many different implementations of this in a variety of different genres, but I think I will stick to RPGs for my examples. Almost every New Game+ mode falls in to one or both of two different categories, depending on the kind of benefit it gives the player. I suppose I will call these the Carry Over type and the Bonus Prize type.
Carry-Over type New Game+ modes allow you to carry stats and abilities from the end of the game to the beginning on a subsequent playthrough. Chrono Trigger, many of its direct imitators like Shadow Hearts, as well as many recent games like Nippon-Ichi's Disgaea games, use a system of completely carrying over your party's full capabilities from the end of the game to the beginning of the next playthrough, so you can begin the game with characters strong enough to defeat the final boss. Other versions let you only carry over a specific set of things from one playthrough to the next. For example, in Suikoden V, you can keep money, unequipped items, formations, epic skills, and Party SP, but not levels, experience, or anything equipped or spent on a character. In SRW: OG2, I was able to carry over three times my reserve of unspent money and half of the total amount of Pilot Points obtained for each character. Both of these two effects are similar in concept, but the difference in degree has a pretty significant effect on the game.
With a partial Carry-Over benefit, the game is a bit easier than it was on the original playthrough, but otherwise it tends to play a lot the same. The main effect is to make playing through the game just a bit easier the second time around. My second playthrough of Suikoden V was very similar to my first, and was possibly even more difficult in the end because of some poor choices of tactics on my part. My current playthrough of SRW:OG2 is almost identical to a normal playthrough, with the exception that I have a few more fully-upgraded units and many more characters have the SP Regenerate ability this time around. These kinds of New Game+ benefits work the best when the player might want to go through the game a second time whether or not there was a benefit. I played Suikoden V a second time because I wanted to recruit all 108 characters and actually get the best ending, and I am playing through SRW:OG2 so that I can see the alternative paths that I missed the first time through.
With a full Carry-Over benefit, the game is a lot easier than it was on the original playthrough. Often, this will result in the complete removal of the normal challenge of the game, and in the worst case scenario it reduces the whole game to a tedious exercise in simply going through the motions. This kind of benefit will only really work if there is new content available filled with challenges appropriate to fully powered characters in the subsequent playthroughs. Chrono Trigger sets a good, if a little simplistic, example of such a good implementation with the way it lets you challenge the final boss at any time on a later playthrough, rewarding you with different endings depending on where in the story you do so. Many other games that use this benefit don't provide new challenges or other new content, and thus tend to not work as well as other New Game+ modes.
Bonus Prize type New Game+ modes don't let you carry over anything from your previous playthrough, but provide a totally new benefit instead. One of the clearest examples of this is seen in the SNES game Lufia 2: Rise of the Sinistrals, where you will receive four times the experience and money from every battle when you start the game with the Retry mode, with no other change. In Fire Emblem: Path of Radiance, if you go through the game a second time you will be able to acquire special stat-modifying equipment that you can't get otherwise. In other games, going through the game another time will let you see plot scenes or story paths that were not open to you the first time. These kinds of New Game+ benefits try to make the second playthrough different than the original, so playing through the game again feels like a new experience.
Overall, I think New Game+ modes are great for adding replay value to a game, but they require that the game either has multiple routes or possibilities that encourage replay in the first place, or that the New Game+ mode opens up new game experiences. If all the New Game+ mode does is let you go through the exact same game, except without any challenge, then it will not add to the game experience at all.