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I've got Webers, not Dels, but the two should have similar cold start characteristics.
I'm with Gordon. I've never seen a car with either of these carbs 'race' on cold start - it's usually just the opposite. And the most obvious explanation (there will be others) is that something is 'sticking somewhere', as Gordon suggests.
Here's a simple thing to check. Find the idle stops on your carbs. On each one, there will be an adjustable screw that holds the shaft of the carburetor open just a bit at idle. (This is how you normally set the idle speed.) You should see how the shaft comes to rest against the screw. Make sure the fitting on the shaft that's supposed to contact the screw is actually doing that for both carbs when the throttle is released.
You can check this with the engine off. The shafts of both carbs should return all the way 'home' (against the idle stop screw) after the throttle is opened, slowly or hard, and released.
It could be something inside the carbs that's hanging up (or something completely different), but this is a simple thing to check for starters.
The shafts on both carbs should move freely, with no binding, through their whole range of motion. With Webers (I don't know about Dels), depending on what type of throttle linkage you have, sometimes the internal springs of the carbs aren't strong enough to close the butterflies reliably at idle, and external springs must be added. It's possible that one or more of your return springs may have broken or come loose.
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