I quite agree that the two competitions champions league and premier are two different leagues and a team performance in one can not determine there performance in the other leagues however saying that premier league is more difficult than champions league is something I won't agree . Champions league is a very tough league and I believe is even more tougher than champions league. The fact that Chelsea was lucky to have won champion league when they were unable to win premier league doesn't mean champions league is not a tough competition. A team can decide to shift there attention to a league they consider to be tougher than the other and as such there performance in the other may not that be all good.
I don't really know much about your past discussion but the fact that you said Chelsea Champions League was based on luck is actually disrespectful.
We defeated top teams then including Real Madrid and not like luck played everything for us in the final. We lacked the consistency to win the league and Manchester City who is often the most consistent team in the EPL in recent years lift the EPL, while we defeated them deservedly in the Champions league.
Our squad depth then were so great even to our substitute lists, where even a scary starting eleven could be made. This was one glorious season of Chelsea before the fall and we are still trying to bounce back, I guess you might have forgotten how good/excellent Chelsea were before the whole Todd Boehly era, where we are still finding it hard to find our fit again.