Why does Samuelson say common stocks are better than bonds and preferred stocks during inflation?

This was most likely reference to the Fisher hypothesis. As argued by Engsted & Tanggaard (2002):

classical economic theory, especially the Fisher hypothesis, according to which expected nominal asset returns move one-for-one with expected inflation such that expected real returns are independent of expected inflation. A related implication is that assets which represent claims to real payments, such as common stocks, should offer a hedge against unexpected inflation, while assets which represent claims to nominal payments, such as bonds, should not be expected to offer such hedge possibilities.

Essentially this is because payment on both bonds and preferred stocks are usually fixed nominal terms. For example, bonds pay fixed coupon payment that is predetermined at a time you buy bond. Preferred stocks also usually stipulate some dividend payment that is fixed. This means that inflation makes the value of the principal as well as the fixed stream of coupon payments/dividends lower in relative terms.

Moreover, as explained here bond prices fall when nominal interest rises and vice versa.

$$ P = sum^T_{t=1} frac{C_t}{(1+i)^t}+frac{M}{(1+i)^T}$$

Where P is the price of the bond, C is the coupon i the interest rate, and M the value at maturity (i.e. the face value). By Fisher equation $i approx pi +r$ where $pi$ is the inflation rate so as inflation rate increases the market value of the bond will be lower. Furthermore, as explained in this investopedia article proffered stocks are very similar to bonds except for legal treatment that is unrelated to this particular discussion. This being said bonds should according to theory still offer hedge against expected inflation because rational person would take any inflation expectation into account before investing into bond (although of course in real world people's expectations might not be completely rational).

A common stocks essentially represent claims to real payments as mentioned above and hence they should offer better hedge against inflation in general as they should also cover the unexpected inflation.

However, few caveats:

1. The empirical literature actually does not confirm the above result. See for example, . Fama and Schwert, 1977, Gultekin, 1983 or Barnes et al. (1999). The Samuelson's textbook was first published in late 40's even though it is being regularly updated with new edition it might be that this statement was not updated or perhaps Samuelson wanted to teach people about the Fisher hypothesis - that is up to speculation.

2. Inflation adjusted bonds and floating dividend preferred stock exist, but I think that Samuelson was implicitly talking about the 'standard' bonds and preferred stocks. Although of course we can only speculate about what Samuelson was thinking the passage would not make sense otherwise.