The Anniversary graphics setting for Halo 1 and 2 have become borderline unplayable since Reach dropped in December. Larger levels have drops that may be 30 fps or lower, based on my best estimate. Going into any large level and looking at an open area is guaranteed to tank the framerate. Switching to original graphics does seem to basically lock the game to 60 fps though. Additionally, checkpoints are causing huge hitches in every game in the MCC, besides maybe Halo 4. All of these issues seem to have begun with the Reach update in December. Thus far, I don't believe that 343 has acknowledged the issue. My experience has been limited to the Xbox One X version.
Halo 1 and 2 Anniversary Frame Rate Drops