An emulator and a launcher are different tools
Dolphin is the GameCube and Wii emulator. It is open source, and its netplay, widescreen hacks, and texture packs are years ahead of a generic launcher. If the only games you care about are GameCube and Wii, install Dolphin and stop reading comparison tables.
RetroApp is the shelf around many consoles, including the ones Dolphin does not touch: SNES, PS1, GBA, Mega Drive. It is not a replacement core for Metroid Prime. It is where Prime sits next to Chrono Trigger and a friend who does not want a second tutorial.
Netplay, honestly
Dolphin's netplay is built for Dolphin. Traversal, save sync inside a session, and a community that already knows the rules. RetroApp's sessions are for the library as a whole. For a GameCube night with people who already use Dolphin, use Dolphin. For a mix of 16-bit and PS1 with people who will not install three emulators, use RetroApp.
Do not expect Dolphin's widescreen codes or frame-advance tools inside a launcher. Those stay in Dolphin. RetroApp's job on that system is artwork, a save that is not trapped on one disk, and a way back to the rest of the library when the session ends.
Using both
Keep Dolphin updated. Point RetroApp at the same dumps if you want them in the shared library. BIOS is a non-issue for GameCube in the way it is an issue for PS1: Dolphin does not ask for a PlayStation BIOS, and neither should your launcher.
The same split applies to PPSSPP if your backlog is PSP, and to DuckStation if it is PS1. Specialized emulators win on their one machine. A launcher wins when the evening is more than one machine.
Download RetroApp · BIOS guide · Save states · Best retro launcher · vs LaunchBox · vs Playnite · vs EmulationStation
RetroApp vs Dolphin is a launcher comparison. Specialized emulators stay better at their one console. The table above is the feature split. The text is the part that should decide the install.