In my experience, it's usually the capacitor that pops, but my experience is mostly with GU10 form factor bulbs, which have the downside of being very compact and fitted in fittings that don't have good heat reduction properties resulting in everything running hot, even in a LED bulb that should be cool. Even the cheapest LEDs last longer than standard halogen GU10 bulbs though, so there's that.

Capacitor usually blows - they don't like operating really hot and heat removal inside those small form factors is a serious challenge. Also, many times, the whole power converter is encased in a semi-insulative rubber, so that just compounds the problem.