There are a couple of things the 3ds could do better than the Gamecube-Wii, such as shaders. This is a result of it being slightly more modern tech. It also had significantly higher ram and higher storage capacity than the Gamecube mini disks allowed for. But it is still overall a weaker system when it comes to number of polygons and texture quality. Comparing it to the Wii, it still has more ram, but the difference isn't as pronounced, and the Wii could push even more polygons and better textures than the Gamecube since it was more powerful in every way than the cube.
Not that many games really took advantage of what the 3DS could really do. Capcom's Resident Evil and Monster Hunter games, Kid Icarus Uprising, Mario 3D Land, Metal Gear Solid 3, Dragon Quest 8 and the fighting game trio of Smash Bros. Super Street Fighter 4, and Dead or Alive Dimensions are the only games that come to mind as really pushing the system and showing off its strengths. Resident Evil Revelations in particular is so advanced that it's hard to see it running on the Wii and especially the Gamecube without significant downgrades to its shaders. One thing I'm not sure of is whether the 3d effect ate graphical resources that could have gone to things like polygons and textures. I know there were games where it hurt the framerate or resulted in anti-aliasing being turned off.
What we see in Gamecube ports to the 3ds is interesting. Luigi's mansion has small downgrades from the original, and the Melee levels in Smash 4 are basically 100% conversions. Both were launch window Gamecube games, so not the biggest hardware pushers, while the 3ds versions launched later in the system's life and seem to be among the most advanced games on the system. I'd say that the 3DS at its best could push what you'd expect from a very early Gamecube title, but that would include Rogue Leader, which was very much a hardware pusher and probably far beyond what the 3DS could handle.
The New 3DS had one major flaw that held it back - they didn't improve the GPU performance at all. This meant that older games didn't run any better and was a serious bottleneck on getting the most out of the improved CPU and ram. The CPU allowed for much better performance as well as more enemies on screen in Hyrule Warriors and the ram allowed for better textures in Monster Hunter 4 than the same games for the base model. But very few games take any advantage of those improvements. Xenoblade was in my opinion a bad choice to show off the upgraded system's power because while it was impressive to see such a huge game on the handheld, the 3ds was never meant for games like that and the big environments were wasted on the small screen, Plus it had one of the worst uses of 3D I've seen on the system. Resident Evil Revelations looked as good as it did because it kept the environments small and packed with detail.