I can only get a 1 1/4 inch receiver on my current vehicle, and my last one. I have a two bike rack from Thule, and have had no issues, including multiple 800+ mile day trips. With a 1 1/4 inch receiver you are limited to a two bike rack. Other than that, it is no issue. Just get a good receiver. The receiver made for my vehicle by Curt, required a special strap if a bicycle rack was used. The receiver I bought, from Reese did not, as the Hidden Hitch receiver for my last receiver also did not require a strap.
Of course if a vehicle can accept a 2 inch receiver, go with that, you can then use 1 1/4 or 2 inch.