Exactly how often does this explosion happen, and is it a 2.50 meter
radius, or 2.50 meter diameter?
It is neither diameter nor radius but rather area which gives you a radius of roughly 0.9 meters. The description states that the explosion covers 2.5m which lends itself to area not distance from point of impact. My proof would be a screenshot of it in action if I had a PC (sorry I have a console and could not get a picture). The explosion is roughly the same size as a husk is tall and it is rather chaotic. It is simply is not large enough to say it has a diameter of 2.5 meters.
As for how often, again it says it in the title - intermittent. It does not occur every shot nor after some timed interval. Sometimes it takes several bursts of an assault rifle and other times I get two or three explosions in a single burst. Using a pistol I typically get an explosion once every 2-5 shots. It is also worth noting that the bullet must hit an enemy for the explosion to occur. Think of it like a passive version of incinerate that occurs randomly when you have incendiary ammo active.
The reason I ask is because I'm having trouble with whether this will
be worth giving up a whopping extra 12.5% damage.
I have used both perks and I can guarantee you will not be disappointed with explosive burst. The extra damage is nice of course, but explosive burst is by far the more useful perk. For one thing the AoE damage is very effective when enemies are grouped together (while experimenting to write this answer I took out three husks at once). Also, it seems to have a force associated with it which staggers enemies with shields and can throw unshielded enemies to the floor. It looks awesome in action and is best used with an assault rifle or SMG in burst or full auto.