In compensation for these downsides, you would expect to be paid more. As an hourly rate I'd say two times the hourly rate of an FTE doing the same job at that company is customary, common, and generally considered reasonable.
Example -- so someone at that company is making $60,000 / year doing that job, that is $30 per hour. You would expect $60 per hour as reasonable, since you get no benefits of any kind. With this approach and income expectation you can make a reasonable career out of this manner of consulting. (You'll be able to pay for your own benefits & vacation, cover the risk of sudden termination, etc).
If for some reason they are paying the same as they would per hour for the FTE (and saving on the benefits too), then their goal in this situation is simply to save on labor costs.
The first situation cited - payment at 2x the hourly rate of a comparable FTE - is a standard contractor rate. You can do OK if you can collect this kind of rate consistently.
The second situation cited - payment as a contractor at the same rate of hourly pay as an FTE - is really temping.
Temps are notoriously low paid. And they are insulted regularly in business culture. Temping is part of an attitude that a certain individual is not good enough to be hired as an FTE so they are paid through a labor agency as a temp.
Contracting is to earn a real living. Temping is for survival.
There's also kind of a mental readiness component to contracting, too. It's the war between middle class humility and what you ACTUALLY need in order to earn a living.
The rate differential given above (also stated sometimes as 1/1000 of your target yearly income) is the
bare minimum that you should accept as a contractor.
This is to work as a surrogate employee but be paid as a contractor. To not have books written by you, inventions, patents, or some huge landslide of industry accolades. This is to be an ordinary Joe (or Jane) worker who happens to be a contractor.
2 times the normal hourly pay of a FTE worker. No less.
Rates appreciably above that level are for highly specialized developers in particular niches.
You have to be comfortable asking these rates. NOT feel that they are "too high." Clients will try to chisel your rates.