There is a growing demand for accurate high-resolution land cover maps in many fields, e.g., in land-use planning and biodiversity conservation. Developing such maps has been traditionally performed using Object-Based Image Analysis (OBIA) methods, which usually reach good accuracies, but require a high human supervision and the best configuration for one image often cannot be extrapolated to a different image. Recently, deep learning Convolutional Neural Networks (CNNs) have shown outstanding results in object recognition in computer vision and are offering promising results in land cover mapping. This paper analyzes the potential of CNN-based methods for detection of plant species of conservation concern using free high-resolution Google Earth ${}^{\mathrm{TM}}$ images and provides an objective comparison with the state-of-the-art OBIA-methods. We consider as case study the detection of Ziziphus lotus shrubs, which are protected as a priority habitat under the European Union Habitats Directive. Compared to the best performing OBIA-method, the best CNN-detector achieved up to 12% better precision, up to 30% better recall and up to 20% better balance between precision and recall. Besides, the knowledge that CNNs acquired in the first image can be re-utilized in other regions, which makes the detection process very fast. A natural conclusion of this work is that including CNN-models as classifiers, e.g., ResNet-classifier, could further improve OBIA methods. The provided methodology can be systematically reproduced for other species detection using our codes available through (https://github.com/EGuirado/CNN-remotesensing).