The differences between a 1.5hp and a 2hp Puch are listed on the Puch horsepower differences page, but the 1hp models had a few restrictions all to themselves. This page explains and shows those restrictions. Some 1hp models may have slightly different restrictions than what is listed on this page, so if yours has a restriction that isn't listed, take a picture and add it.
The intake port on the 1hp cylinders is severely restricted where the intake attaches and/or inside the bore.
The intake itself on a 1hp cylinder matches the restrictor and is therefore very small.
The 1hp cylinder has an extra-thick head gasket, which reduces compression. Replace it with a skinnier one, or if you have a good seal between head and cylinder, remove this gasket completely.
The exhaust port may or may not be restricted. If you want to figure it out, compare this picture to the ones on the Puch cylinders (aluminum series) page.
However, the exhaust itself MAY be restricted. This pipe came from a Sears Free Spirit, and this restriction is not necessarily found on all 1hp Puchs.
Other potential restrictions include a longer piston and an airbox restriction.
To check for the piston restriction, rotate the flywheel until the piston reaches TDC. Then unbolt the intake from the cylinder and look through the intake port into the cylinder. If the piston skirt does not completely clear the intake port, this is restricting the cylinder. You can correct this by marking the exposed part of the piston skirt, then griding it off.