I have two vector data sets - one is in NAD27 and the other is in WGS84. Normally I reproject one at a time. But can I just use 'batch project' to reproject both of them to NAD83 at once? I was not sure if the input datum must be the same for all files.
I don't believe I've ever tried it but you can set the Geographic transformations in the 'Environment Settings' of the Batch Project Tool (see attached screen shot). Note: You will have to figure out which exact transformation you require (depends on the geographic area you're dealing with. The '_6' for example is for a specific region. See this page for more details: About Geographic Transformations Hopefully this helps. Let us know if it works out for you.