India - Traveling between Agra and Jaipur

I was at the Houston Travisa Outsourcing office picking up my India tourist visa. I chatted with two gentlemen who visits India regularly. One suggested that instead of travel between Agra and Jaipur by train or by car, it can be faster to return to Delhi from Agra and fly to Jaipur for Delhi.

What do the experts on this board suggest? What is the best way to travel the Del, agra and Jaipur triangle?

By car or train no point going back to Delhi
Car more flexible on times

Go by train. Would make no sense to transit Delhi. Even car will be long and difficult. Train is best. If you can afford it helicopter charter is a good option in that region depending on the number in your party.

returning to delhi makes no sense....car or train between agra - jaipur is better before returning to delhi....

Train, it is. Thanks for the response.

What about Jaipur and Johpur? What is the best mode of transport between the cities?