I rarely have DILD and have been able to WILD much better. Do DILD’s feel different than WILD’s after you acheived lucidity? I had a DILD but it felt quasi-lucid since it was very strange but i was able to still manipulate my dream really well. But a couple things were very strange like having a wolf head as my hand. . or the dream felt unfocused and was shaking but i wouldn’t wake up, but would fall into a normal dream… I hope i’m getting close to having more consistent DILD"S. Anyone else experience the same thing? Because when I do a WILD i’m fully lucid right from the start and can maintain lucidity really well.
When more experienced with DILD there is no bigger difference then in WILD.
Stability can usually be different because with WILD you consciously entered the dream when in DILD you become conscious while in a dream and things can get a little bit strange like you said…
I look at this as when in DILD we need to get the dream in “order” when with WILD we can have this order from the start, more or less 
.
So DILD can be a little bit strange at the beginning but when you get more experienced in this then DILD can be as any other WILD!