How do you choose between simple random and stratified sampling?

One thing to consider is that you choose a simple random sampling from an homogeneous population. Imagine that you're making a soup. How do you know if the taste is good? You take a spoon. Why? Because the soup is homogeneous so any soup you take, from anywhere of the soup will have the same taste. That's simple random sampling.

Simple random sampling may be the easiest conceptually but, in practice, difficult to pull off. The benefit is that randomness is, by definition, uncorrelated with the things we want to measure; the procedure tends towards unbiased estimates. However, if people are not 100% mandated to participate when selected, there is a chance that the factors correlated with (non)response will also be correlated with the outcome of interest, in which case the measures will be biased. To take an example from political polling: when partisans perceive that their group isn't doing well, they're less inclined to take surveys focusing on politics. This depresses the estimates of support for that side because people with a bone to pick will still respond.

One excellent source of information to base strata estimates (in the US at least) is Census or other government sources. Much of it is freely available online. Not all government surveys will provide optimal estimates to base your strata off of (it's important to read the documentation when making your decision) but it can often be a great resource when employing stratified sampling in practice.

Within the real world, it's often very difficult to ever implement a general Simple Random Sample strategy. Feasibility aspects such as cost, size of your sampling team and population accessibility all affect the general use of SRS as your primary sampling strategy. Moreover, it's a grossly inefficient method of sampling when you're dealing with large samples over a wide geographical distance. Finally, it's important to note that even when stratifying, you're still using SRS after you've stratified the sample. For example the population is divided into smaller groups, or strata, based on ethnicity and then a simple random sample is then taken from each stratum in direct proportion to the size of this ethnic group compared to the population.

Also, I would possibly add the idea that stratification can be used to artificially boost a certain stratum beyond what is actually present within a population. Let's say you want to compare differences between ethnicity by some other variable, well when you stratify you can then sample an equal proportion from each stratum and then compare. In the normal population you may find that there is a greater proportion of one ethnicity than another, but maybe thats not what you're interested and actually you want to compare these two groups by some other variable of interest. In that example, stratification is used to balance groups for adequate comparability.