I agree that Chubbys is WAY better than Red Iguana. RI may be authentic Mexican, but it's too authentic and spicy for me. The Shred Beef Plate tastes like shredded prime rib and gravy that melts in your mouth. The Shred Beef can also be ordered in tacos and burritos too. My wife loves their rice and beans. Both are subtle, and always good. The Chubbychanga is good, too. The ambience kind of sucks, but if you like good food, in a quiet setting (unlike Red Iguana) at a reasonable price (from $5.50 to $7 for most dishes), this place is authentic Mexican comfort food.
I've tried a lot of Mexican food restaurants in SLC, for example the Rio Grande Cafe near the Gateway Mall, and the Red Iguana on N. Temple, and they come nowhere near the quality of food at Chubby's. My office has a regional office located in Denver, and the regional execs frequently travel to SLC from the Denver office to do work in our field office and when lunch time rolls around, there's always a discussion as to where we'll all go for lunch, and invariably when folks want Mexican food, Chubby's is the first choice, even through we have to drive past The Rio Grande Cafe or the Red Iguana.