Am building a house, 28' x50'... 2 floors, fairly open floor plans, 9' ceilings.
High performance windows, doors and insulation on Cape Cod.
What would my air conditioning requirements be?
How many BTU would serve me?
I am looking at LG ductless systems... Mitsubishi too, but don't know which to choose.
1 or 2 zones?
I have installed radiant infloor heating system...
What would you recommend?

Allot of good information except for what part of the country you live in. I would use two zones, up and down. What about the master bed, upstairs or down?

[I] Did say we were building on CAPE COD
2 floors
Master bed upstairs

Two 1.5 ton units would do well.

Take a set of your plans to a good heating and AC company and have them figure a "Heat Loss'" for you. Lot's of variables in determining how much heat you need and the same about cooling. Such things as Shade, Which direction does the house face, how many trees, how much glass, what kind of roof.

[I] Did say we were building on CAPE COD
2 floors
master bed upstairs
Oh, sorry I took it as a cape cod style house. 1.5 ton should do

Any decent HVAC contractor will do a load calculation for free, don't guess on this one.
Spend all that time and money and then not be comfortable in your own home. Find someone
Who will put in writing exactly what you need and what degree of temp you will get from your new home comfort system. Both brands are decent in my opinion. Look for good warranties.
Check out the LG art cool, Looks like a picture or painting