  The Chabauty--Coleman method is a $p$-adic method for finding all rational
points on curves of genus $g$ whose Jacobians have Mordell--Weil rank $r < g$.
Recently, Edixhoven and Lido developed a geometric quadratic Chabauty method
that was adapted by Spelier to cover the case of geometric linear Chabauty. We
compare the geometric linear Chabauty method and the Chabauty--Coleman method
and show that geometric linear Chabauty can outperform Chabauty--Coleman in
certain cases. However, as Chabauty--Coleman remains more practical for general
computations, we discuss how to strengthen Chabauty--Coleman to make it
theoretically equivalent to geometric linear Chabauty.
