The stock SD-1 sounds a bit thin. You could have it tuned by Keeley or analog man to get a fatter sound.
The SD-1 is not a good pedal, imo.
However, it may be that you have the Tone control on the OD set to a position where it's accentuating some frequency you don't like. Have you tried working with the Tone knob?
Also, try playing your guitar with the SD-1 in your signal chain but
off. Are you still experiencing the same problem?
Have you tried a fresh battery? A dead battery can wreak havoc on your tone!
Finally, try setting the controls on the SD-1 in their neutral position. Toggle the pedal on and off. Are you hearing a difference?
Unfortunately, unless you practice at gig volume regularly, it's hard to know ahead of time what your tone will be like. There are always some small tweaks needed when you get to the venue, since each room is different.