NORMALLY they will be the same price. Advance/online purchase of tickets for train travel in Belgium involves no price advantage, unless:
a) you are under 26 (GO-pass-1 ticket) or
b) a "web deal" fare is available for your date of travel (as currently applies for TRAVEL - not just purchase - during the period 9/10 - 4/11/2012),
given that both these types of fare can only be purchased online - whether in advance or on the day of travel - and so are not available at the station.
But, if a lower offer subsequently becomes available for the date in question (for exemple, "summer ticket" or the "shopping ticket" likely to be announced next month for weekends in December and weekdays between Christmas and New Year) it is perfectly possible to pay more by buying in advance, rather than less.
Also, whether purchasing in advance or on the day, you will have bought a ticket for travel on a particular route on a particular day, but not on a specific train (departure), as already explained by Colin56. It is not possible to reserve seats for train travel in Belgium, unless you are a group; so you will not actually have "pre-booked" anything by buying online/in advance.
So if you do buy online, there is no need to worry about missing the train you intended to catch, unless of course your flight is so late that you could not continue by train on the same day. On the other hand, you would pay exactly the same price (€19.10 standard single, €38.20 return but for specific date - there's no such thing as an open ticket) if you left it until you reach BRU to buy your ticket(s), subject of course to the considerations set out above.