It is fair to say this is quite distorted by the impact of very low interest rates on expectations of future profits though, which is a key component in the share price.
Also, at it's peak Standard Oil was worth about 6% of the US stock market. Apple is currently worth 5.3%. This comparison should be robust to differences in interest rates. In this light, Apple is slightly smaller than Standard Oil was. But, the market is broader now and there are more lines of business in existence. So a company that dominates an entire line of business would be expected to have a lower proportion of total stock market cap now than in 1910.
At the very least 2021 Apple and 1910 Standard Oil are very comparable in size. There might not be a clear way to tell which is bigger.