The size and type of tag to use depends on the application.  Here are some things to consider.

Smaller tags have less impact (weight, volume) but have shorter read range compared to larger tags.  Large tags are easier to read.

Half duplex antennas are simpler and easier to build.  The power consumption is lower due to pulsed charges rather than the continuous field used by FDX.  HDX speeds are controlled by the reader and can be slowed down to extend the battery runtime.  The maximum read speed with a 50 ms charge pulse is 14 scans per second.  Shortening the charge time can increase speed further but may not fully charge the tag.

FDX tags repeat their tag numbers 30 times per second.  FDX tags have fewer components and can be made thinner than HDX ones.  The funnest FDX glass tags are 1.25 mm diameter.  The thinnest HDX is 2.15 mm.