First, I would recommend the approach of designing your own custom format (binary data is normally faster, for instance) for loading into your app. That custom format should be designed for efficient loading - both in time and matching the internal format of your stored data. I find that most available modeling program export formats don't entirely meet the needs of my app. E.g., the data is arranged differently than I desire, or my code has to process or combine data to fit my app's storage scheme. And, often, export formats are text-based (.x, xml, etc.) which can be more efficiently loaded in binary format.
If you create a custom format and use that for loading animation data into your app, you'll have to code a converter to read/parse/process modeling program each desired export format to your custom format. Even if you use only one input format, loading efficiency can probably be improved by that conversion.
In addition to loading data more efficiently (as mentioned), that approach provides the means to use different modeling programs which may or may not export data in a "common" format. Further, in the past, I found that different modeling programs export files in a "standard" format (.x, md5, etc.) but the contents differed either in arrangement or actual data content. Another benefit is to reduce the need to revise your graphics app if you want or need to revise the conversion process. Your graphics app can have a single loading routine - good for debugging!