Any title using .vff files to store content will greatly improve in SSD when loading/saving. The most noticeable is creating a new save file in SSBB or in some N64 VC titles (like Paper Mario 64). When running Dolphin in HDD the FPS will suffer a huge slow down (FPS 0 -2) while the save file is being created (and that can take around 5 minutes in some cases) and later on you may get micro stutters while saving (at least in SSBB). I'm not sure, but the stutter you're getting when you connect to Nintendo WFC in SSBB maybe related to that too...
Avell A70 MOB: Core i7-11800H, GeForce RTX 3060, 16 GB DDR4-3200, Windows 11 (Insider Preview)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)