I would say it's always better to register on time because you have more possibilites to build a stack. Sometimes you can late reg but I wouldn't do it if you start with less then 50bb's or so.

Of course the structure of the tournament is important. If you buy in to a tournament that's a turbo variant and you start with 40bb's, you'll get way less chances to improve your stack and it is possible that you'll bleed down to let's say 10bb's without even getting a hand.

I'd always advice to buy in on time because of the above reason.

Late reg will generally raise the chance of cashing but can decrease the chance of winning, as you will mostly be forced to gamble sooner. One notable exception is bounties, as some of you equity comes from knocking players out their is an advantage to be had every time you can achieve a ko in a hand. If the average chips has advanced much you won't initialy be able to win any bounties. Another factor is hourly, this is easiest to demonstrate with limit tornie. At the start you can only win small amounts that, depending on the structure, will have only small effect on overall equity. You may then be better playing another Mtt if available and Reg latter. The same is true on some Nl/Pl tornies but usually the chance of doubling through week players early reduces the effect. Live I see more of an argument for late registration as you get the time back. My local casino has trended toward deep and steep tornements with 15-30k starting stacks. They play 3 30min levels 25/50,50/100,100/200 then jump to 200/400 after. If I go for start I loss 2 hours of Time 3 levels + 30break. Or I can have my evening go late and sacrifice minimum equity.