Same as Chas despite having a decent Meddings drill press. Quick and easy on the lathe and I can count on one hand the number of times it's been even slightly off centre. I don't experience blow outs either.
The only time I would consider the drill press these days was if I was using a seriously "banana" shaped blank.
If you do a search on the forum, the subject has been discussed and argued about at great length and you'll probably get all the information you need. Best advice is use the method that suits you personally.