##BCl_3## is the stronger Lewis acid.
We would expect ##BF_3## to be stronger because ##F## is more electronegative than ##Cl##.
Chemists explain this unexpected result by an electronic argument and a steric argument.
The electronic argument backbonding
The boron atom in ##BF_3## is ##sp^2## hybridized with a vacant ##2p## orbital.
The ##F## atoms can also be ##sp^2## hybridised with lone pairs in their ##2p## orbitals.
These ##F## orbitals can overlap with the orbital on ##B## thereby increasing the electron density on the boron atom and making it less acidic.
This effect is called backbonding because electron density is leaving the more electronegative atom.
In ##BCl_3## the ##3p## orbitals on ##Cl## are bigger than the ##2p## orbital on ##B## so orbital overlap is less efficient and backbonding is less important.
Hence the greater backbonding in ##BF_3## makes it a weaker Lewis acid.
The steric argument ligand close-packing (LCP)
The LCP model is based on the observation that the ##X## atoms (ligands) in ##AX_n## systems are always the same distance from each other.
For example the distance between the ##F## atoms in ##BF_3## and ##BF_4^-## is 226 pm despite the longer ##B-F## distance in the tetrahedral structure.
(from alpha.chem.umb.edu)
It is as if the ##F## atoms are closest-packed (like in a crystal) with the ##F## atoms having a ligand radius of 113 pm.
When the ##BF_3## forms a Lewis complex the ##F## atoms remain close-packed but the ##B-F## bonds must become longer in the new tetrahedral geometry.
(from http://pubs.acs.org/doi/abs/10.1021/ic990713m)
It takes more energy to lengthen the short strong ##B-F## bonds than the longer weaker ##B-Cl## bonds.
Hence ##BF_3## is a weaker Lewis acid than ##BCl_3##.