Most multiplayer characters are more powerful than Shepard, especially Levels 1-20. Shepard needs more levels to overtake the advantage of gear, amps and ammo in MP.
If you have played MP enough to be experienced, you will be able to get through Insanity most likely. There are some key differences:
-Enemy max HP was similar to Gold at the release of the game, but Gold HP was raised with balance changes.
-100% shieldgate for enemies on Insanity vs 75% on Gold and Platinum. The variety of weapons with which you can one-shot protected enemies in multiplayer, especially given the superiority of MP anti-shield ammunition, is much higher than in SP where it is largely limited to shotguns and the Talon, as well as basically one build on Infiltrator with the Javelin.
-Unless you have paid DLC weapons, the weapons in SP are going to be worse than in MP simply because of level cap and the necessity to level those accessories through the game. If you play NG+ this is less of a concern.
-The two main differences that make SP appear easier than MP is the lack of timed objectives and the fact that fights are usually spread further apart with fewer enemies.
-The N7 side missions are a decent comparison between SP and MP based on mechanics. Start a new character on insanity and go to Sanctum as soon as possible for an example. However, you won't get spammed with Phantoms like in the unbalanced MP waves.