How many of those sides from "lesser" nations ended up winning it or even getting to the final? The major countries always held sway only the Champions League allows a greater spread of winners from those countries which makes it harder to win and nigh on impossible to go back to back. I agree though its an achievement whenever anyone won it.
Malmö, Bruges, Partizan Beograd, Panathanaikos all played in European finals, Red Star and Steaua Bucharest won the European Cup.
Depends how far you want to go calling things "small leagues" - no Dutch or Scottish team will ever win it again bar a complete sea change in European football.
Even in terms of diversity from "big" leagues - Liverpool, Nottingham Forest, Leeds, Aston Villa all competed in the final over a certain space of time, but could only do so because they'd put together squads good enough to win the league, not finish third or fourth in it.
Saying the "major powers always held sway" is tautological, they are the major powers because they hold sway. You can see from the off that the Spanish and Italians valued European competition much more so than the insular British.
I'm not the older era was harder or easier - just different. It's very difficult to legitimately compare the Lisbon Lions to todays Celtic team who reached the last 16. Moreover I consider it a pointless comparison anyway.