Hi Khushboo,
In my opinion it will be a decision based on time. For example, most customers do not encounter any issue during the upgrade, and if this is the case, it's best to do direct upgrade as it is time saving. The downside would be that you have to rollback each time after you hit an error. If multiple issues are hit, we usually resolve them and apply same solutions in advance for any subsequent upgrades on higher level environments.
If you do progressive install, it will require taking full database and file backups after each stage, which can be quite time consuming. It will save you time only in case you hit multiple issues as you can work them through one by one, without doing a full rollback.
I generally recommend going with direct upgrade, and seeing how it goes. It is a rare occasion that we at Support recommend to customers to do progressive upgrades, and it is always having a specific reason for it.
Considering your specific path 12.1>13.1>13.3 : there is absolutely nothing wrong with it, but in my opinion it would be more helpful to actually do 12.1.0 > 12.1.1 > 13.3, as this has been the path I would usually recommend to customers for progressive upgrade (12.1.1 stage would not require a rollback so if something goes wrong during first stage, we could fix the issue and re-run the upgrade straight away).
Please let me know in case of any more questions.
Kind Regards
Nika