I've roundtripped my Honda ST1100 from Canada to Europe twice now (three sectors by air, once by ship) and am just getting ready to send it Canada-Europe again, by air.
The cost varies depending on the origin and destination airports chosen. It has less to do with distance than it has to do with the availability of belly space in widebody aircraft that serve the charter (package tour) market. Weight of the moto is not an issue, because the 'cubic weight' (space occupied) is always far greater than the scale weight.
The average cost for me to ship my moto from Toronto to Paris by air is about USD 1,300, one way, using Motorcycle Express. I could ship it myself on the same air carrier for about 20% less, however, my experience has proven that MC Express more than earns their fees in the services they provide that reduce hassle and smooth the procedure out. NB I work in the airline industry, so it would not be a problem for me to do all the paperwork myself. But, it would be a problem for me to miss my passenger flight due to some glitch in the freight process that MC Express would just look after for me, long after I have departed.
Forget shipping by sea (via the north Atlantic) - it will be far more expensive and far more grief than air freight.
It seems that the break point for renting at destination vs. shipping your own happens at about 3 weeks. For less than 3 weeks, rent. For more than a month, ship.
Hope this helps.