Preferred shares are much like a bond when it comes to the impacts in terms of interest rates. They're often thought of as a hybrid stock/bond investment. Not very many retail investors own preferred shares. In fact, they're mostly owned by institutions.
Much like bonds, they have a par value and can trade at a premium/discount to that value. Although preferred share values will fall when rates rise, and rise when rates fall, typically it's less amplified than a bond.
There are a multitude of options when it comes to preferred shares. In fact, a ton of investors simply get lost in the options and avoid them altogether. Callable, floating rate, cumulative, participating, non-participating, convertible etc.
The main pro of preferred shares is higher income and more stability than a common stock. And, in the event of company liquidation, you'd be paid out your capital before common shareholders would, but after bondholders. Keep in mind, more stability does NOT mean no volatility. We saw many preferred share prices collapse during the market crash, especially of companies in poor financial position.
The cons of preferred are obviously you do not get to participate in the price appreciation of the company themselves. For example, we've saw a company like Enbridge gain over 35% in price this year, while some of its preferred shares are up around 5%~. Another con would be you don't get to participate in the bonus earnings growth of a company, as your dividend is typically fixed. So say Enbridge has an outstanding year and can afford to bump the dividend 10% instead of 5%, you'll see nothing from this. And a lesser con, because most don't even utilize their right anyways, is you have no voting rights as a preferred shareholder, unless you buy one that includes rights.
Overall the simplest way to put it is it is a hybrid investment of a bond/common share. You will gain added income and more stability, but sacrifice overall returns, voting rights and dividend growth.