The difference being that the two AA "leagues" in baseball are shaped around the majors, and are on equal footing. There is a huge gulf in class between the ECHL and the CHL because the former has NHL backing and higher payrolls.
The main reason you won't see a "championship" series between the two leagues is money. Most times the league champ and runner up in the ECHL end up losing money on the final series due to the amount of travel on short notice. Buying 25 plane tickets a day or two in advance is never cheap, plus all the luggage a team has to carry ends up being a surcharge. To add another series with long travel on short notice for those two teams just wouldn't work financially. (Plus the fact mentioned earlier that the union contract specifies when players are done for the season, and adding on would require changes there, plus very likely another month in the team paid apartments. The income from three or four games against a team in another league probably isn't going to cover those costs (plus payroll, insurance, ice time, arena costs, etc).
Unless two teams that were geographically close together felt it would make money and were able to put it together quickly and convince the players (or pay them a big bonus), the only way I see that happening is if the two leagues merged and it was the actual final playoff series - and there are too many differences between the two leagues at this time for a merger. Unless one league is really in trouble I don't see it happening. Both of them feel they have the better business model for their situation. I don't know about ECHL teams moving to the CHL, but there are certainly some teams in the CHL now, who wouldn't qualify for membership in the ECHL. After some of the situations the last few years the ECHL has toughened up their requirements for owners.