My understanding is that current GA piston engines from Continental and Lycoming are based on a design from the 1960's. There have been many evolutionary improvements, but only within the limitations of those 1960's designs. They are large displacement (~1.5L/cylinder), run at RPMs in the mid 2000s range so that they can spin the prop at optimal rates without using a gearbox, and they are air cooled to save the weight and complexity of a liquid cooling system.
What would a completely new, designed from the ground up GA piston engine look like today? Factoring the massive improvements that have been made in all sorts of engines over the years in non-aviation applications- for autos, trains, boats, generators, etc.
Would they still operate at such low RPMs? Yes reliability and durability are still major concerns, but manufacturing tolerances are so many times smaller now then they were in the 1960s (possibly allowing for reliable operation at higher RPMs), and they are now mounting fixed gearboxes to commercial airliner turbine engines so adding a fixed gearbox to a GA piston engine should be trivial.
Would they still be air cooled? Yes it can still save weight, but possibly at the cost of extra cooling drag, and definitely at the cost of much more finicky operation that requires the pilot to carefully monitor engine temps throughout their flight cycle.
Would they still be in a flat engine arrangement (flat 4, flat 6, etc.)? I would imagine so, I can't imagine an alternate piston engine arrangement with the smoothness, packaging, and scalability advantages of the flat architecture. Straight engines get too long, and V engines require many more changes to scale the number of pistons up or down.
Would they still fly on spark-ignited gasoline-type fuel, or could compression ignition based on jet fuel produce the power density and reliability required? I realize that the single largest factor in this area might be the simple availability (or lack thereof) of fuels, but I am talking about purely from an engineering perspective. Suppose we are talking about North America where both Avgas and Jet A are widely available, what would be the superior fuel for flying GA piston engines?
What other differences might there be that I haven't considered?