Though the GameCube & Xbox eventually both died out in place of their successors, the PS2 remained too hot to ignore, while the PSP's successor (the Vita) wouldn't come out until late 2011. Therefore it made too much sense to continue releasing games on both pieces of hardware, which included games that were also releasing on the newer consoles. For the most part these "HD" games also came out with "SD" versions at around the same time, but there were some examples where the PS2 and/or PSP version wouldn't come out until a fair amount of time after the initial HD version came out; in other words, they were (as some would say) backported from HD to SD. So let's go over some examples of games that were designed for the PS3 or 360 first, only to later get backported to the PS2 and/or PSP; i.e. no simultaneous releases here!
We start off with a batch of titles, mainly because if I had included them individually it would have made up 2/3 of this entire list, and since they're all part of the same overall franchise it's better to just put them together; also, it was these games that inspired me to make this entire list. While the first entry in Koei's iconic Dynasty Warriors/Musou franchise was actually a 3D fighter for the PS1 back in 1997, it wasn't until the second entry in 2000 (which is technically the first in the Shin Sangoku Musou spin-off series, hence why they're always a number higher outside of Japan) that the concept of it being a 3D hack & slash taking place in various open battlefields was truly established. In 2004 developer Omega Force introduced the first true offshoot of the series with Samurai Warriors, which traded in the Chinese Three Kingdoms setting for Japan's Warring States era, and since then the franchise has spun off to include the likes of Fire Emblem, The Legend of Zelda, Fist of the North Star, One Piece, & many other licensed IP. In 2006 the Musou franchise started getting released on HD consoles with Xbox 360 ports of both Samurai Warriors 2 & Dynasty Warriors 5, though the latter was only released in Japan, and in 2007 saw the release of both Dynasty Warriors: Gundam (which was based on Sunrise's iconic mech franchise) & Warriors Orochi (a crossover between Dynasty Warriors & Samurai Warriors), which launched on HD consoles. However, the PS2 & PSP still saw love from this franchise, with Warriors Orochi being released on both Xbox 360 & PS2 at launch worldwide, which in turn made a PSP port natural since it could be based on the PS2 version. The same is more or less true of 2008's Warriors Orochi 2, so neither of those count for this list.