here's some very rough ideas.
a) if you are in with a chance of an early legacy victory (3* nearest rival), then convert, purely for the legacy gain;
b) if you are playing Rome be careful due to the civil wars as a young/stable Empire, try to make your control over your regions as secure as possible before converting;
c) assuming that you are facing all 500 turns to win by legacy then think carefully about when to shift. In theory you only have 3 more govt changes (ie age reductions) and usually you go through young/stable at some speed (as you drop the age related part of the decadence calculation), so you can face a long time with age increasing apart from maybe the civil reforms decision or any remaining objectives. Here you might want to delay at Civ Level 2 for a while and make the change when in a while.
d) but even as a glorious Empire you can set up a old/stable/glorious shift by manipulating your culture output, you don't want to do this too many times but it can be handy (and of course as Rome you are back to risking civil wars when stable);
e) Empire gives some very nice trade related bonuses, if you are a trading faction it can move you to a very dominant position (especially if linked to the trade decisions).
Its probably the major decision in the game