Does mining in a pool with a bigger hashrate mean more bitcoins? Will someone with a 800&nbsp;Mhash/s device earn as many bitcoins in one day as someone with a 10&nbsp;Ghash/s device?

(I can't add a comment to 
Mining pool hashrate effect on a miner&#39;s income
so I'm asking here.)
No, payments are distributed proportionally to the contributed work.

The chance to find a block is proportional to the hash-rate of a mining entity. So, if watched sufficiently long you could expect to get the same percentage of all rewards as the portion of the total mining power you contribute. This principle remains the same whether you solo mine or pool mine (minus any fees the pool costs you). 

However, the pool combines its power to find more rewards, which it distributes among its contributers according to the size of the contribution of shares to the pool. I assume the operator gets a percentage of the reward in some fashion. That way you gain a steady small income instead of winning the lottery every few decades.

So, whether we are talking about mining pools in the network or participants in a mining pool, if watched for a sufficiently long period of time the entity with 10 GH/s will earn 12.5 times the amount of the entity with 800 MH/s.