It’s really important that you choose one option or the other. The most immediate difference between them is that backups made to iCloud use up some of your paid-for storage allowance. If you’re already using most of that and would need to increase your subscription, that’s a significant step. Although you don’t pay monthly for storage on your Mac, you still need free space there.
Both types of backup exclude most of the data already stored in iCloud, such as Contacts, Calendars, Notes, iMessages and text (SMS and MMS) messages. Neither do they include data from Apple Mail, or content purchased through the App Store, Music or Books. iCloud backups don’t include Activity or Health data, although they’re always encrypted; if you encrypt your backup to a Mac, that will include both.