A traditional synth doesn't usually have built-in song sequencers and recording functions such as found in a DAW. But I'll assume you're referring to synths and "workstation" keyboards that do have built-in song sequencers and recording functions.
Some people who have an expensive higher-end workstation arranger keyboard say that its built-in song sequencer and recorder is all they need for recording. They're able to record MIDI tracks one at a time, edit the tracks on a note-by-note basis, add a vocal track by plugging a microphone into the keyboard, balance the volumes and stereo panning of the tracks, apply effects, and then convert the song to an audio file-- usually an MP3 file.
Of course, the exact capabilities and editing functions of the built-in song sequencer can vary from one keyboard model to the next, as well as the number and types of effects which are available, whether an audio track can be included, whether the song can be converted to an audio file, etc.
Similarly, DAWs can differ quite a bit from each other as far as things like maximum number of audio and MIDI tracks, the number and types of included effects and virtual instruments, the overall user interface, etc.
So it's partly a question of the particular capabilities, functions, and user interface of the song sequencer, and partly a question of what a person has gotten used to. Some people get to be very proficient at editing a MIDI track note-by-note on a keyboard, and if they try switching to a DAW they can feel like a fish out of water. Other people are more proficient and experienced at working in a DAW, and if they try switching to a keyboard's built-in song sequencer they can feel like tearing their hair out in frustration.
Of course, another option is to combine both approaches and get the best of both worlds. The built-in song sequencer makes it easy to quickly record tracks without worrying about mistakes. The tracks can then be imported into a DAW for editing. Some DAWs even have notation views that let you edit a MIDI track as notes on a staff. Then the tracks can either be mixed down in the DAW, or transferred back to the keyboard for conversion to audio. Finishing up in the DAW can let you use virtual instruments and effects that aren't available on the keyboard, or that are available but don't sound as good. But if you're using the keyboard's voices and effects then finishing up on the keyboard can be simpler than having to transmit the final MIDI from the DAW to the keyboard and simultaneously record the keyboard's audio output in the DAW.
Note that some synths-- as opposed to workstation arrangers-- don't really have sophisticated or full-featured song sequencers. Instead, they may have functions and controls which are designed to be used with a particular DAW.