With one prize.. chances when one prize, 1 ticket out of 300 versus 2 tickets out of 600?

you just divide it, the probability of winning when there are 300 tickets is 1/300=0.0033 for both cause the other one the division is the same

If you know that there is exatly one winning ticket then the probabilities are the same, as Roberto said. Similarly, if you are sure that when you buy two tickets they are not the same ticket, then again the odds are as he said. However, if there's a chance that there are duplicate winning tickets then your odds go down a smidge if you buy 2 out of 600versus 1 out of 300, because you might actually buy two winning tickets and yet win only 1 prize (depending on the rules of the raffle).