I would not recommend either process as there might be references to other projects/pages/nodes which you might remove not knowing.
The best approach will be to go to Touch UI and delete it from there. You can look into deleting at a parent level folder if you would like to do it in one go. But this process will make sure all references are properly removed and no issues are observed later.
I'm not an AEM DAM expert but I'm going to give my opinion.
Many things happen when you delete an Asset. I assume those processes are triggered by listeners on the JCR but I can't guarantee that that's the case.
For example, if you choose to delete an asset via the TouchUI, you benefit from a reference-check that makes sure you are not deleting assets that are in use. Here is an example:
If you haven't already, i strongly suggesting testing this first using the delete dialog or the References rail.
However, if you are just deciding between manual deletion in CRX DE vs deletion by cURL, it's the same thing. In both cases you will send a HTTP request to AEM to delete a node. The only difference is that in CRX DE you have the chance to change your mind before you commit XD