Lightroom certainly does - no idea about Capture One as have never used it.
Lightroom has import presets, development presets (recipes) and export presets. They can all be applied to single images or batches.
Development presets - LR comes with a bunch of presets and many people have released their own for download. Plus of course you can save your own. Like the way that you have processed an image? You can save all the settings as a user defined preset.
Development presets can include any of the following settings...
White balance, exposure, contrast, highlights, shadows, white clipping, black clipping, tone curve, clarity, sharpening, saturation, vibrance, colour adjustments, noise reduction, and on and on....
Import presets - These can be applied as/when you first import images. I have an import preset which will automatically...
1. Create a folder for the images (date as folder name)
2. Copy the images from the card to the folder
3. Rename the images [custom suffix]-[Year]-[Month]-[Day]-[original file number].
4. Automatically apply a Development preset (approximates Canon's Camera Faithful settings) as a starting point for processing.
5. Automatically set the colour label to green for all the imported files. - I have all my RAW files labelled green. If I then create a virtual copy I label that yellow. Any jpeg, tiff or other image files are then labelled red. Allows me to see at a glance which ones are the originals.
6. Automatically add the keyword "to-do".
I have a LR Smart Collection configured to include any images that have no keyword or have the keyword "to do". That way I can quickly find any images I forget to keyword.
You can of course create multiple import presets so you can have one to put your 5D images into one directory and another t put your 7D images into a different folder.
Export presets - As with import presets you can create a number of export presets. Select a batch of images, right click on them and select which export preset.
As with import presets you can select from a host of settings including placing the files in specific folders, renaming them, resizing them, setting the file format, the colour space plus a bunch more.
In short there is a host of batch processing that can be done, which saves a huge amount of time when dealing with large numbers of images.