Is there any difference between '01 and '03 engine?

No,it will not work,however you can use a 2001 or 2002 engine.. or a earlier engine from a sebring or stratus, you will need to use the pt upper & lower intake, the pt oil pan and oil pump and oil pump pick up tube, in 2002 the head gaskets and head is different than the 2001, but the engine will still work using the 2002 head on the 2002 engine

Can a motor out of a 04 pt cruiser fit in a 03 pt cruiser

This will not work! I tried this one myself with the same years involved on the advice of a chrysler dealer tech that it would work byswapping the upper intake. He was dead wrong. The crankshaft positioning sensor is in a different spot on the block and the lobe it reads on the crank is also different. It can not read correctly to time the engine. You cant swap the computers to make this work either, and also the o3 does not have an egr valve and the 01 does. It all comes down to the computer cannot read key components of this engine. An 01 and 02 are the only years that will fit your car.

What you need is a Hollander book that tells you what the difference is in the engines there may be just little diff and it will tell you what you can swap .
and most salvage yard have these books and dont charge to look it up for you.
and dont let someone guess and say yes and then you have to go back and change so importaint part.
later
paul