Go for the Photoshop. Photoshop can outburst the beauty of your photo. Photoshop consists of so many tools that can make your photo improved than before. I think corel draw doesn't help you to edit your pictures but you can create pictures with it. This is only based on my experiences with this apps.
I have tried both platform, each platform gives a unique with there user interface. although they might be somewhat similar, it still depends on the person using it. personally I prefer photoshop for photo editing. maybe because I feel that photoshop have a lot more users and it is so much easy to find tutorials that you can use. on the other side corel may not be as popular as photoshop but there are also some corel features photo editing.. although you may find it hard to get tutorials for corel.
I am more familiarized in Photoshop so basically I use photoshop than corel when it comes to editing and drawing. If I only wanted to enhance the pictures, I use lightroom for that. It is up to you because there are some people who prefer corel but I think photoshop is more convenient and popular I think but it is really up to you. When I tried corel, I find it hard to navigate the tools since I am more familiarize with the tools in photoshop.
Adobe Photoshop is very user friendly, quick keys are very easy to use since the sequence of drawing patterns are considered in the placement of Photoshop shortcuts. I am using Adobe Photoshop CS6, and it has serve me well. Also the compatibility in exporting to other image platforms is considered, I have minimal issues with image conversions. The quality is not compromised when compressing image outputs. The diversity of usage in image editing is very wide.
Unfortunately photoshop is the best. The interface and layout make it the best to use. They just make it easy to use especially since essentially you can just right click and find the tool you need. I found myself getting frustrated with corel for task that should be easier. I love a lot of the brush use on corel though. I wish their was a good medium between the two because of the cost of photoshop but I don't think that will happen.
I have Adobe Video Collection and Corel Video Collection. If I'm doing a lot of expensive editing, I make use of Photoshop. It's slow to tons, yet it has degrees of ruin, masks as well as basic power of raster data. If I have a lot of fast photos modifies, I want to utilize some fashionable filters on the image or making GIFs/PNGs, I such as Corel Photo-Paint. It loads faster and works quicker. If I'm processing my trip photos as well as wish to proof, crop and do straightforward edits, I utilize Adobe Lightroom. If I want to "draw" on a picture, I make use of Metacreation's Painter (which is now owned by Corel). It's unbelievable for the variety of brushes and textures for when the picture is just the beginning factor.