Over an infinite period of time Solo Mining will be more profitable than a mining pool which charges fees. Over a shorter period of time random luck figures in so there isn't a clear winner.
At 1GH/s and current difficulty you should get about 0.66BTC/24hr period (deepbit's calculator).
Envelope calculations ahead:
Deepbit is at 3800GH/s and finding a block every 30minutes.
With solo mining at the current difficulty 1GH/s should take about 80 days to solve a block, so you have a 50% chance of earning 50BTC in 40 days.You could also find 10 in a row as soon as you start, or not find any in your lifetime.