You have to embark and go through border checks 30 minutes before departure with Eurostar, that's a fact. Whether you will have to answer questions is very random and doesn't seem to depend on whether you give them a passport or just French ID. My wife has a Canadian passport and a French residency permit and this does make them ask more questions though.
Eurotunnel checks were lighter when I used to take it, but that was before the Calais crisis so I would guess it has become more bothersome lately.
In any case, you just can't say it's as easy as just hoping in your car and driving to Belgium and back to fetch your beer.
Schengen agreement mandates no border check, but the UK is not part of it, so of course they can have border check
I guess I misunderstood what was being talked about, but I was actually trying to make the point that movement between Shengen and the UK is different from movement within Shengen.
Specifically, I was answering to this exchange:
>> it was always more difficult to go to/from the UK
> This is not true.
by saying that it is actually more difficult to go to/from the UK. Which it is.