Regardless of whether you're solo mining or pool mining, as long as it's the same coin, your expected number of coins per day should be the same (minus a pool fee). However, the benefit of mining in a pool is that you reduce variance greatly. For example, let's say you have enough hashrate to mine 1 LTC per day on average. If you solo mine, the expected time to find a block is 50 days, but that doesn't mean you will find a block in 50 days. In fact, you might not even find a block in 500 days. It's all random. However, if you're using a pool that finds a block every 50 minutes, the probability that it goes for 500 minutes without a block is the same as the probability that you, as a solo miner, go for 500 days without a block. So you can expect more regular payouts with less risk, making the pool fee well worth it in my opinion unless you alone have 1% of the total network hashrate or something.

As for how the estimated number of coins per day is actually computed from your hashrate, see my answer here.