Billiards room drink holders compared
A rail attachment and a side-table base do different jobs.

Table-attached holders
Check the pool table maker’s restrictions and accessory attachment method. Do not assume a clamp is harmless to the rail or finish.
Wall shelves
A broad secure shelf can serve drinks if it stays outside cue movement. Measure depth and access rather than only available wall space.
Steadi on a side table
A compatible drink gains a wider resting footprint without attaching anything to the billiards table. It still remains an open drink.