So, is it best to take photographs when it is overcast and shadowy or in bright sunshine?
Well, in most cases (although not all) bright sunshine isn't the best for taking pictures of flowers, or indeed pictures of anything. This may seem a bit counter intuitive but pictures taken in bright sunshine can look harsh, with strongly contrasting areas and dark unsightly shadows. This is not usually the type of appearance that best suit flowers. Flowers look better in a softer, more gentle kind of light.
The early morning or later evening sun produces a much softer light which works very well with flower photography. If you find you are out in bright sunshine you can improve your image by placing the subject matter in shadow - this can be done by position yourself between the sun and the flower or by using an object (coat, magazine, rucksack - what every you might with you) to shield the flower from the direct sunlight.
In the image at the top is of the same flower taken at the same time on the same sunny day in April. The first image was in taken in bright sunshine. The second was taken whilst shielding the flower from the sun using a piece of cardboard. The second image is slight gentler and softer in nature - more appropriate for flower photography.