Deep learning (DL) techniques have emerged as promising solutions for medical wound tissue segmentation. However, a notable limitation in this field is the lack of publicly available labelled datasets and a standardised performance evaluation of state-of-the-art DL models on such datasets. This study addresses this gap by comprehensively evaluating various DL models for wound tissue segmentation using a novel dataset. We have curated a dataset comprising 147 wound images exhibiting six tissue types: slough, granulation, maceration, necrosis, bone, and tendon. The dataset was meticulously labelled for semantic segmentation employing supervised machine learning techniques. Three distinct labelling formats were developed -- full image, patch, and superpixel. Our investigation encompassed a wide array of DL segmentation and classification methodologies, ranging from conventional approaches like UNet, to generative adversarial networks such as cGAN, and modified techniques like FPN+VGG16. Also, we explored DL-based classification methods (e.g., ResNet50) and machine learning-based classification leveraging DL features (e.g., AlexNet+RF). In total, 82 wound tissue segmentation models were derived across the three labelling formats. Our analysis yielded several notable findings, including identifying optimal DL models for each labelling format based on weighted average Dice or F1 scores. Notably, FPN+VGG16 emerged as the top-performing DL model for wound tissue segmentation, achieving a dice score of 82.25%. This study provides a valuable benchmark for evaluating wound image segmentation and classification models, offering insights to inform future research and clinical practice in wound care. The labelled dataset created in this study is available at https://github.com/akabircs/WoundTissue.