They do have discretion and they don't always properly check (it can also depend on how long ago your offences were, as they may not be readily available to them). Also the deemed rehabilitation (where you are automatically considered rehabilitated after 10 years) will still be considered for old offences before they changed the law in 2018. Flying in is usually better as they are more hesitant to turn you around as they have to get the airlines involved (the airline has to pay for your return flight if you are denied entry). But don't freak out if they bring you in for secondary screening, and just answer them truthfully and fully, they always prefer that, and it shows you're not hiding anything and not a menace. When you are driving up, they have no hesitation in turning you around since you just turn your car round, it's a lot less screening for them, and they are in their rights to do it.