There are other reasons that cycling is less popular there . Prague is a big walking town, with about 20% of all intracity trips being by foot. The terrain is a bit hillier than in Budapest and public transport, due to larger subsidies and a more sensible time-based ticketing system, is more affordable.
But in the coming years, we can expect Prague to close at least part of the cycling gap with Budapest. For one thing, Prague is spending serious money on cycling -- about EUR 2.5 million annually, an amount that has grown steadily over the last seven years, from the time city leaders agreed once and for all that cycling should be a priority. This amount is about double what Budapest is spending, despite the fact there's much greater interest in transport cycling here.
The other thing is that the guardians of Prague's historically protected centre have capitulated on the bike path dispute. After the disastrous floods of August 2002, the pedestrian quay along the east bank of the Vltava River had to be rebuilt, including with new cobblestones. The original reconstruction didn't include a cycling path, but after activists laid on the pressure, City Hall agreed to a solution in which twin tracks of smooth, tan stone were laid down the cobblestone korzó. The tracks are very narrow -- maybe 50 cm -- but they provide bump-free passage through the cobblestones while also blending in with the rest of the stonework. This accomodation demonstrated to the cycling naysayers in the historic district that bike paths needn't detract from the Prague's Medieval charm.
It seems to me that this type of compromise could serve as an example to other European cities that struggle to reconcile historic preservation with modern development. This includes Budapest, with a prime example being the main square at Óbuda. The north-south cycling route from Budapest to the Danube Bend cuts right across this square, and it's the least pleasant part of the journey because of the cobblestones. Another example is Andrássy út, where the cycling paths on both sides of the street intermittently cross cobblestone bus stops.
These are examples of when biking accomodation doesn't necessarily have to cost more, but rather just needs to be given some consideration before roads are built.