President Obama intervened in a crucial referendum. President Trump did not.
Some commentators see symmetry in the interventions anti and pro Brexit by successive Presidents. There is one crucial difference. President Trump is not intervening in an election or referendum, whereas President Obama deliberately tried to influence voting. Most of us think a government leader should not try to influence an election in another democracy during an election period. As it happens, I think it was an ill judged intervention, as it added to the unreality of Project Fear and ended up helping the Leave campaign.
The other difference with Mr Trump’s intervention is his is a factual statement. Were the UK to accept the White Paper position it would be much more difficult to agree a Free Trade Agreement with a non EU country. President Obama, on the other hand, was saying he would seek to delay a UK free trade agreement which would otherwise have been possible. The Trump Administration would like to do a free trade deal with us, but can only do so if we leave the EU, single market, customs union and surrogates for them.