Really it depends on what you want to do later in life. I mean they're both great programs. I think fulbright is more prestigious sure but its only 8 - 9 months. Jet could potentially go on for 5 years. Jet also pays really well - better then fulbright. But I see jet as setting a career trajectory towards teaching english wherer as fulbright has name recognition and prestige that would aid you anywhere you go. Also, having lived in japan for a few months I ca,e away with the impression that though it is an awesome place to visit, its not a place to set down roots. Besides being damn near impossible, the japanese are very ethnocentric in their thinking making acceptence there a rare thing for a foreignor. I felt like any time I spent there, though exciting and amazing was a waste of time in terms of my overall life goals because I could t make anything permanent work there. Where as with the fulbright you could be making contacts that could lead to something amazing and exciting. O it could be as transitory as jet. Really its up to you. If it qere me I would go for the fulbright. But then again I applied for a full grant that will earn me anm MBA. I sujppose as an ETA you'd be doing similar if not the same think as you would on the jet program. Except jet lasts longer and pays better. Hmm.
Also id argue with the whole competitveness thing... I thin k jet is more competitive - especially since it has been declining in recent years while demand has been increasing. Last year there were over 5000 applicants for about 1500 spaces. I applied two years running - made alternate the first year and nothing the second year.