Hi, dont compare the courses on the amount of training, focus on the quality of the training. May I ask who the training providers are that you are looking into? a 16 week course might sound better, but there's plenty of people on this forum who've been disappointed with their college course because the tutor isnt knowledgeable, and the classes are large so they dont get much 1 to 1 time with the tutor and work their way through their course blind.
I'm not saying that your 16 week course will be crap, only that there's as much chance that the 4 day course is a quality course as with the 16 week one. Instead of looking at the length of course, find out some more information about the content. Find out who your tutor will be and what their qualifications/experience are, find out how large the classes are, find out how the classes are structured, what products they use, how they assess you, there's loads to ask. You could always ask for reviews on here if you dont mind sharing with us the names of the training providers you are looking into.
Personally I can recommend becoming a CND tech. It's the leading name in nails, generally its the brand your clients will recognise which is important, and both the products and the training are of very high quality. I know things have changed since I did my training, but when I trained we did 4 full days in the classroom, then a month later we did another full day, then 6 weeks later another classroom day. We were assessed on the 5th and 6th days, and we practiced at home in between classroom days, but essentially there were only 6 classroom days, and the training was very high quality. It just goes to show that shorter training courses can be good provided the quality is there.