Factologically false on both accounts.
Even second tier la liga teams have been more successful in Europe than most first tier pl teams for a decade or so, while second tier english teams have been utter rubbish, irrelevant. You don't see Arsenal, Tottenham (one lucky fluke) or Everton coming even near to be challenging against top tier of Europe on year for year basis.
Spanish teams have dominated entirely because of their technical ability that has been honed in spanish culture of football for decades and come to maximal fruitation in recent decades. Best achievement by spanish teams have been made, while playing technically and often also tactically superior football, which successfully neutered the physical superiority of opposite teams. Golden era Barca vs MU was typical example of that. Currently it's just that there is major generation change and footballers that were dominating the 10s are withering away, while next generation is just forming. There was never problem even "overpowering" the so called physical teams, which is evidences how Barca and Spain could apply relentless and tenacious pressing through all 90-120 minutes, completely exhausting and choking the opposite sides into complete submission. Again, it's all about players.
Ironically enough there has been lot of spanish influence on english football in recent decade, which has enriched both style and player/coach content of it, while bleeding away some good blood from la liga. It never happens the other way around. UK doesn't produce world class footballers that often. Their league largely rely on big money that can buy foreign talent in players and coaches. Not much of an achievement sporting wise.
