The shelter spay clinic prices are usually due to the following:
1. volunteer or reduced fee by the operating vet;
2. assembly line process for the day - getting the most bang for the buck so to speak;
3. minimal after spay care - they go home the same day, often while still groggy from the anesthesia (depending on the animal's position in line for the operation);
4. cost of supplies only and/or subsidized by grants/donations.
I have had animals spayed/neutered both ways (regular scheduled vet appt and reduced cost spay clinic). I've never had any issues either way.
If you are unsure about signs of problems after surgery, then you would probably be more comfortable with the regular vet surgery. If you are comfortable with keeping an eye on the cat (watching for signs of distress, shock, messing with incision, etc.), then you would probably be fine using the clinic.
One thing I do recommend is that if you use the low cost clinic, ask about donating to their cause. Even if you donate an extra $40, you are still well under your planned expense and that will provide spays for two additional cats that might not get it otherwise.