What are the key differences in giant and large unilamellar vesicle preparation processes?
Giant unilamellar vesicles (GUVs) are made by methods like hydration of phospholipid membrane generally by use of some solvent , use of electric current, combining small vesicles etc. 
large unilamellar vesicles (LUVs) are made by methods like evaporation with low concentration of phospholipid, dialysis etc.
Small unilamellar vesicles (SUVs) are made by methods Injecting solution spontaneously, microfludic methods etc. There are many methods reviewed extensively (just search in pubmed you will get lot of them)

Now coming to your question, factor which affect sizes are depends on method you are using. I will list out few, rest you can check in references of each method I gave above. Most of times these methods will have all kinds of vesicles. Success of these methods relies on which method gives you highest proportion of vesicle size you desired. 


Microfludic method - total flow rate, ratio of solvent to aqueous phase (Kastner et al 2014)
Electric method - rate of application of electric field (Angelova and Dimitrove 1986) 
Hydration method - amount of phospholipid, evaporation rate (Lasic 1988)


Besides all of this, basic physics behind this explained here like energy difference shown below 
(Image taken from (Lasic 1988))