BMP files are uncompressed and typically larger than TGA, because some TGA files use run-length encoding (RLE) which, while not exactly an effective compression method, does usually reduce image size slightly.
I'm sorry to depart from the thread topic but I couldn't leave
Neither TGA or BMP are a good idea to use for forum; TGA because most browsers can't natively view those images (which means forum bbcode can't show them either), and BMP because they are simply uncompressed, unaltered bitmaps. Images don't get bigger than that. However, I heavily recommend saving screenshots as TGA (or if possible, PNG). You definitely want to have a lossless source image to work from, whatever format you end up uploading to the interwebs.
As for whether JPEG or PNG should be used, both have their places; however, for game screenshots I would exclusively recommend using PNG with high compression. It results in a lossless image that usually only has slightly larger file size than a JPEG of same image, if acceptable (highest quality) compression settings are used.
If there's a problem with loading times of forum posts, it's generally better to take the time to post thumbnail images that link to full-resolution images, rather than reduce the JPEG compression quality - especially in the type of images posted in this thread which are supposed to demonstrate/test a specific graphics issue.
It's almost impossible to determine whether the anti-aliasing is actually working because the JPEG compression itself fuzzies everything up. So it would be good to see HotelAlpha's screenshots in PNG...