This thread may turn into a minefield by the end of the weekend, everyone will have their favorites......
HID is cheaper to purchase, but expensive to run and needs replacing sooner. The spectrum of light is not on the money but pure intensity makes up for that. The heat produced is problematic needing a lot of other equipment, BUT it has a very reputable history that is documented time after time.
LED is the newcomer and earlier lights promised so much that HID fans revolted. The spectrum is spot on, it is cool to run and uses less electricity.
Induction lamps are not new, but they seem to be becoming more popular and have a long lifespan, have a good spectrum and are cool to run.
Ask yourself first what you want to upgrade to based on the amount of plants you want to grow and how many in what style.
Hope that helps...