What size and type of dry fly and what rod and line are you using? As a general rule, casting large, bulky dry flies very far or with line control on UL gear can be difficult. Your leader taper and length may also be critical factors in turning over many flies.

Because the wooly bugger has less air resistance than a parachute adams. Size 14 should be fine for a 2wt. You didn't say what tippet, but you might try cutting it back a foot or so, or making a two-stage tippet, such as one foot of 4X and 2.5ft of 5X.

Your problem is difficult to understand, it may be that the wooly bigger was a little heavier and turned the loop over easier. As mentioned above your leader and tippet may be the answer. I find a lighter fly is easier to cast and will give a softer landing/ presentation. Are you finding it harder to shoot line or is the presentation not as good as you want or expect?

In general, I experience the same problem when switching from a heavier fly to a lighter fly; coincidently, I often switch from a wooly bugger to a dry fly. Here's my take on the problem and my solution.
The problem is more pronounced when I am casting against a breeze, even if the wind is so light it doesn't ripple the water; this is some insight to the problem.
The wooly bugger absorbs water and this weight allows shooting the fly; the momentum of the fly carries the line thru the cast. To explain what I mean by shooting the fly, on my last cast I have line in my left hand which is pulled through the guildes to complete the cast. In that last cast my arm delivers more energy from the 12 to 9 position than when I cast the dry fly.
When I switch to the dry fly, in my case a Norm Wood or Stimulator, I do no shoot the fly; if I do then the leader will coil up at the end of the cast. My cast with the dry fly consist of false casting until the fly is over the target and then letting the fly, leader and fly line decend to the water with no line uncoiling from my left hand.
I would say the wooly bugger is delivered horizontally and the dry fly delivered vertically.
If I am casting with the wind, the problem is less pronounced but still persists.
As suggested, shorting the leader mitagates the problem but by changing the casting technique I have been able to stay with the same leader length.
I am normally fishing a #6 or #8 wet or dry fly. I target bass or blue gill and my UL rig is a 7 foot #3 Native Custom glass rod with weight forward fly line. My leader length is from 7 ft to 9 ft and I like keeping the leader length towards 9 ft when fishing dry (thus shortening the leader is a no go for me).

So I made it to the river this morning. I cut my tippet down to about 18". Started out with a nymph and indicator. The started seeing fish rise. So I tied in a black gnat and started casting. And it castes like a dream. It appears that the leader and tipper was too long. Apparently it was losing the momentum of the fly line.