The main difference between 1-inch and 2-inch filters is their lifespan. A 1-inch filter with less surface area will clog up more quickly and need to be replaced sooner than a thicker filter. A high MERV rating could also restrict airflow and cause excessive wear and tear if your system only fits a 1- or 2-inch filter. It's recommended to upgrade to a 2-inch filter or even a 4-inch filter.
Most return air filter grilles accept a 2-inch filter instead of a 1-inch one. The following table lists standard size 1, 2, and 4 inch deep air conditioner filters for your air conditioner, oven, HVAC and Atomic Filters filters. Also listed are the collections of whole-house air filters offered by Atomic Filters. When it comes to a 1-inch versus 2-inch oven filter, you can use a 2-inch filter if the vent is deep enough and it will generally last longer due to more media.
Thicker air filters tend to last longer because they have more square feet to capture and retain air particles, creating charged particles that attract other particles in the air for better filtration when electrostatic filters are used. You can get them at a decent price if you call, as this is actually a very common filter size. Poorly installed one-inch filters whereby air circulates around the frame can be avoided by adding an additional filter or using a permanent filter. Last-line permanent filters are roughly replacements for a cheap filter, as they filter out birds and small children.
You can also use a 1-inch thick filter in compartments that can accommodate a deeper filter.