Asset Price Inflation & Consumer Price Inflation
Well, there are several aspects to this issue. First of all, inflation numbers from the 1970s aren't entirely comparable to the current ones because the methodology has been changed repeatedly, with for example "hedonic adjustment" and "chain-linking" something that interestingly has always meant that estimated price inflation has been lowered. Whether you think all, some or none of these changes are justified is irrelevant because regardless this means that in relative terms 1970s numbers are overestimated compared to current ones.
The most important factor determining whether or not monetary inflation will mainly cause consumer price inflation or asset price inflation is simply what the early receivers of newly created money choose to do with them. They essentially got three choices: to simply hold on to the money, to buy financial assets or use them for consumption. If it is the first, then nothing happens, no prices will increase. If it is the second, then we will see asset prices increase. If it is the third, we will see consumer prices increase. Clearly right now, most early receivers choose to use them to buy stocks and other financial assets.
Then there are other factors that influence the outcome. If we have a negative supply chock regarding for example oil, this will as always mean higher consumer prices, and that influenced outcome of the 1970s. And if politicians pursue deficit increasing policies this will increase consumer price inflation relative to asset price inflation, while monetary inflation combined with "austerity" policies will tend to cause more asset price inflation. The fact that both the U.S. and large parts of Europe pursue deficit reducing policies right now contributes to lower consumer price inflation relative to asset price inflation.