There is little reason to doubt the claim.
There are several possible definitions of space travel. A relatively broad one considers any human who has reached Earth orbit. According to the list of space travellers on Wikipedia, 622 humans have done that as of May 2022.
The usual definitions of the deep sea is the body of water in an ocean in which the sunlight decreases notably in intensity. Of course the exact depth at which the deep sea begins depends on several factors, but 200 m is the generally accepted depth beyond which we talk about the deep sea.
The typical test depth of contemporary nuclear submarines, i.e. the maximum depth for a submarine during peace time, and the depth that submarines go to during sea trials, has been given as 300–450 m. For example, submarines of the Los Angeles-class have a test depth of 450 m, which is clearly already in the deep sea. With a typical crew of about 130 sailors, and with 64 ships that have been or still are in service, and assuming that each ship has reached test depth at least once during sea trials, this line of submarines alone has brought more than ten times as many humans to the deep sea than have been to Earth orbit.
But even if we restrict ourselves to the depths that can be reached only by submersibles and not by submarines (i.e. by vessels that need support of other surface vessels), there is strong reason to assume that the claim is true. There is a large number of different deep-submergence vessels that reach depths exceeding 1000 m. One notable example is the French DSV Nautile, which has a test depth of 6000 m. According to the website of the operator, the DSV has been deployed more than 2000 times under various circumstances. With a crew of three, this means that at least 6000 humans have dived on board of the DSV Nautile. While not every dive will reach the maximum depth, or even the test depth of the vessel, it's certainly not an infrequent thing to do for the Nautile. For illustration, this paper reports on eight dives between 3000 and 4200 m depth, executed in the time span of two weeks in 1985. This short observation time span alone would amount to 24 trips of humans to the deep sea.
To sum up: regardless of whether we use the conventional interpretation of deep sea as any depth beyond 200 m, or whether we extend this to an arbitrary depth of 1000 m or more, there are many, many different submarine and submersible vessels that have been deployed in hundreds or thousands of dives in the last 100 years or so. Hence, it's safe to assume that the number of trips to the deep sea made by humans exceeds the number of trips to Earth orbit by a significant factor.