A sailing ship carrying passengers in the early 1900's would certainly be well out of date. Most passengers would want to have some idea of when they would arrive! That's why steam ships became successful. In those days they were called 'liners', a word that people these days use for the huge passenger ships that sailed in the 20s and 30s. But a liner was a ship that had a regular service, carring both passengers and cargo. Mostly these ships were operated by reasonably substantial firms, attracting subsidies from Governments through mail contracts and the like.

An older ship (sail, sail and steam or steam) operated by an owner/captain would be operating as a 'tramp', picking up a cargo, taking it to an agreed destination and then trying to get another cargo there. Not a lot of use for passengers, and so no accomodation for them.

The earlier steam ships had very inefficient engines and used a vast amount of coal. It wasn't until the later compound and triple-expansion engines that fuel efficiency made longer journeys by steam more possible.

So an older ships would probably have been re-engined (it wouldn't be likely to be crossing the Atlantic with its old engines). And it may be serving ports and countries other than the major ones of the USA, UK and Canada, which would be well-served by the major lines.