They're both lossless. FLAC usually has better compression efficiency.
DTS-HD does have some additional features not found in FLAC:
embedded downmix coefficients
DTS core track, which can be passed through over S/PDIF (FLAC requires HDMI)
less ambiguous definition of channel masks and order
FLAC does define a way to indicate a channel mask, but many players will simply ignore it, and assume the channel layout based on the number of channels
There is currently no defined channel mask or order for 6.1/7.1; for example, HandBrake and MakeMKV don't use the same channel order for 6.1/7.1
HandBrake, 6.1 -> L R C LFE Cs/BC Ls/SL Rs/SR, 7.1 -> L R C LFE Rls/BL Rrs/BR Ls/SL Rs/SR
MakeMKV, 6.1 -> L R C LFE Ls Rs Cs, 7.1 -> L R C LFE Ls Rs Rls Rrs (AFAICT based on my testing)
…neither is correct at this point since nothing is defined in the FLAC specification