The OP definitely seems to be refering to a dodger rather than a bimini.
Our boat came equipped with a dodger, but no bimini. We do have a sunshade that zips to the dodger and ties up to the split backstay. It can be deployed while sailing, but is really more suitable for use at the dock, though we have used it for some refuge on hot Chesapeake days.
I can understand the complaints about a dodger if most of your sailing is fair weather (as mine is), as dodgers do block wind that might be desireable to keep you cool and they can obstruct vision somewhat. We keep the main window panel of our dodger open nearly all the time for that reason. However we do like being able to close it to shelter the companionway if we get weather while at anchor. On our C36, the dodger does not obstruct the winches, but I can almost see that as a deal breaker, if the dodger isn't really needed to shelter the crew and you don't mind closing up if it rains while you are below.
A well designed bimini on the other hand can be a blessing for fair weather sailors as SD points out, since it provides refuge from the relentless sun you get out on the water and makes standing in the cockpit during a downpour less objectionable.
Since the OP's existing dodger blocks the winches, they may want to consider ditching the dodger and going with a large bimini that extends forward enough to cover part of the companionway. This would eliminate the issue with obstructed winch handles, allow better airflow and still provide some protection so the companionway could be left at least partially open if rain drives you below.
However, assuming nothing obstructs the winches, I think a dodger/bimini combo is the most versatile combination for cruising boats and I am planning to add a bimini to our boat that will have a removeable connector to the dodger. The connector will be see through and the bimini will have see through's so the helmsman can see the sails and windex. I will also make sure the frame does't interfere with the primary winches.
s/v Palmetto Moon
1991 Catalina 36