We have had a variety of sizes of pools over the last many years, but 2 yrs of our larger pool - with all of them we use the blue covers, not the cheapest, not the most expensive. With the smaller pools (15', then 18') we saw a greater temp increase due to the smaller volume. We do use panels and have for several years so we try to differentiate the temp differences caused by each. The most obvious is the top 4-6" of water on very sunny days - SUNNY, not just warm because there is no difference there from the cover. Usually we can only tell that before the pump timer has come on or we have water circulation that stirs up that top layer to some extent.

The cover KEEPS my generated heat in the pool
The cover can (but does not always) heat the top few inches of water, mostly only when its hot AND sunny

Another bonus is that the cover keeps additional crap from falling into the pool. I like that part - less cleaning for me.

Cover = good investment