Dual output voltage from zener?
Can it be done with a Zener? Yes.

More efficiently?  NO!!!

Easier? NO!

Is a Zener more stable? Yes, but stability when using LDO is almost never a problem if you just place the decoupling caps as stated in the datasheet.

Any reason to use LDO: yes, all of the above, especially at 200 mA.

I strongly suggest using an LDO.
In case of a zener when the load is OFF and consuming no current, the 200 mA must be dissipated by the Zener which is wasteful and generates heat.
Just don't go that way. LDOs are cheap and easy. Everyone uses them.  Zener diodes were more popular decades ago when linear and switching regulators were more expensive. This cost differential has narrowed considerably.

Feeding the 3.3 V LDO from the 5 V LDO is generally a good idea (not always, see Asmyldof's comment), as it will share the dissipation between the LDOs which is what you want.