The actual bettery life on the DS lite is 12ish hours, 16 if you turn down the backlight. The PSP runs about 4 to 8 depending. Both consoles can use backup batteries.
The best RPGs on the DS are The World Ends With You, Mario and Luigi: Partners in Time, and Final Fantasy IV DS. FFTacticsA A-2, Pokemon games, Etrian Odyssey 1/2, and Crystal Chronicles are also good, but not AAA imo. Before the end of the year, Chrono Trigger DS, and Disgaea DS will be released.
The DS is also BC, in which case you might wanna try out FFVI Advance, The Fire Emblem Games, or Golden Sun, amongst many other great rpgs.
As for RPGs, the PSP is only mildly behind atm, tbh, however, the console has a very poor future lineup of RPGs compared to the DS, and in about 5 months, it will be vastly behind. There is no arguing that point.
The DS is the current leader in great games imo, but at the moment that strength comes more from game selection than RPG lineup, as most of the larger RPGs we know about aren't released yet, but are only planned.
Suikoden, Tales of Hearts, Chrono Trigger, Dragonquest IX, Dragonquest Remakes, Kingdom Hearts, Disgaea, Fire Emblem DS, Sonic Chronicles, Master of the Monsters Lair, Rune Factory, Luminious Arc 2, Ash, Sigma Harmonics, Soma Bringer, and Valkyrie Profile to name a few. There is no question which console is the inevitable undisputed RPG king, and which has more rpg potential.
The PSP has an excellent action RPG, Final Fantasy Core Crysis, already out, but its future RPG lineup is questionable, and The World Ends With You, imo, is the better game, so it's up to the individual user to decide, as always.
However, let me say this, I believe that RPG fans that buy a PSP now instead of a DS, will regret that decision soon, and I've given my reasons why I believe this.