We are traveling to Cracow, Prague, Budapest and Vienna with a group of 10 people. Despite all our research we aren't sure if we can do this best by private motorcoach, especially between Budapest and Cracow or Prague and Cracow or we should consider going by air.

All I know is that travel between Kracow and Budapest is best done by train or bus.
With that many people you really should consider a private driver.
The trip is about seven hours.

Um . . . None of the countries you tagged are in Eastern Europe, they're in Central Europe.

That aside, Budapest to Krakow or reverse is probably more than seven hours considering you'll go through a couple of border crossings. By train, it's 8.5 or more.

You should consider something like this: fly from origin point to Krakow, then go Krakow to Prague, then go Prague to Vienna, then Vienna to Budapest. Depart Budapest to origin point. Krakow to Prague is a haul, but shorter than Budapest to Krakow. And the Prague-Vienna and Vienna-Budapest trips are shorter.

For travelling in Europe I do prefer overnight trains to planes. It is quite safe (especially if you travel in bigger company), often cheaper than plane, definitely more comfortable (almost like sleeping in hotel if you buy sleeping place). You also avoid fascinating boarding procedure and unlike plane, the train brings you straight to the city centre.

Krakow - Prague train leaves Krakow everyday at 9:57 pm and arrives to Prague at 7:33 am.

Budapest - Krakow train leaves Budapest everyday at 7:55 pm and arrives to Krakow at 6:56 am. You can check the schedule for both above trains here: http://rozklad-pkp.pl/?q=en/node/143

Prague - Vienna train leaves Prague (Praha) at 11:28 pm and arrives to Vienna at 6:08 am. The schedule is here: http://jizdnirady.idnes.cz/vlaky/spojeni/

Vienna - Budapest trains depart almost every hour and the trip takes around 3 hours.

If you have not yet bought your air tickets then I would find the cheapest roundtrip or open jaw flight and plan from there. I too would think with 10 people the most economical way would be to hire a driver who in addition could narrate and stop along the way as desired. The only segment I would go via train would be Budapest to Vienna which is not long at all. Depending what time of year you go you could also opt to take a boat between these two cities. I would only do the night train between Krakow and Budapest if all ten of you (!) are sound sleepers. My husband and I did this leg via overnight train a couple years ago and he slept like a rock while I not a wink.

In addition I would encourage you to rent apartments over hotels to give you space to all get together. For Budapest check out the website everythingbudapest.com for lots of great info on the city, Enjoy!