DE lamps use different ballasts. The ballasts are often referred to as "HQI" but "HQI" is used to describe a lot of things. In 250W it means ANSI M80 ballast, but there's no such thing as 400W HQI, but the term is still used. A 400W HQI ballast is really a ballast for a 430W HPS lamp but can be used on a 400W MH lamp. I don't know what ballasts are used for 400W DE lamps.
Anyhow you can run a SE bulb on an M80 ballast. The technical details get quite into the nitty gritty, but basically the voltages and amperages and whatever else is used to drive these lamps are done so at levels closer to European specs, so these tend to be "more optimal" ballasts for a lot of our lights we use in this hobby, because those bulbs tend to come from Europe in the first place (well, originally they did, anyhow, or so I've come to understand). You have to of course understand it's not a fair apples to apples comparison because European electricity is not the same as North American electricity.
50Hz vs 60Hz, 110V vs 220V, etc. etc. etc.
Confused yet? I sure am. Let me try again:
- 250W DE isn't really brighter than say 400W. That's a bit of an urban myth. But the reflectors tend to be very good, so you get a very focused light out of a good DE fixture whereas you might not get that same focus out of a cheap SE reflector.
- DE lamps tend to have a lower profile fixture so they are better in some applications, for sure.
- DE lamps require a "HQI" ballast but the term "HQI" is potentially being misapplied. For a 250W DE lamp you want an ANSI M80 ballast, for a 150W DE lamp you want an ANSI M81 ballast. You can call these ballasts "HQI" and people will know what you mean.
- There's no rule saying you can't try to run a SE lamp on one of these ballasts. In some cases (or all cases (??), I don't know) you will get improved performance on a SE lamp using these ballasts because the ballast is "driving" the lamp (probably not the best term to use, but I'll use it anyhow) closer to its original specs than other ballasts.