Both offer some water protection in the event of siding leaks etc. Tyvek (or any modern house wrap) is a wind barrier. If properly installed (all seams overlapped and taped etc.) it makes a house much "tighter" and prevents drafts and associated discomfort and heat $ loss. The main reason that you do not want to use felt paper on the sidewalls is because it creates either a second vapor barrier or a vapor barrier on the wrong side of the insulation, depending on the construction. Either, or both of these conditions is bad and can cause moisture and rot inside your house where you can't see it. Tyvek and sim. are similar to gortex in clothes in that they stop wind and water but allow the evil vapor to pass through. If the structure will never use heat or A/C then none of this really matters. The above only cover the basic principles involved and should not be considered a 100% complete explanation.
If a builder doesn't know these basics then his knowlege base is antique and you should definitely seek advise from others regarding these matters. There has been significant progress in building know-how in the last 30 years - your builder's refusal to learn about and embrace modern, proven techniques could end up costing you mega dollars down the road.