We would expect "BF"_3BF3 to be stronger, because "F"F is more electronegative than "Cl"Cl.
Chemists explain this unexpected result by an electronic argument and a steric argument.
The electronic argument — backbonding
The boron atom in "BF"_3BF3 is sp^2sp2 hybridized, with a vacant 2p2p orbital.
The "F"F atoms can also be sp^2sp2 hybridised, with lone pairs in their 2p2p orbitals.
These "F"F orbitals can overlap with the orbital on "B"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"_3BCl3, the 3p3p orbitals on "Cl"Cl are bigger than the 2p2p orbital on "B"B, so orbital overlap is less efficient, and backbonding is less important.
Hence, the greater backbonding in "BF"_3BF3 makes it a weaker Lewis acid.
The steric argument — ligand close-packing (LCP)
The LCP model is based on the observation that the "X"X atoms (ligands) in "AX"_nAXn systems are always the same distance from each other.
For example, the distance between the "F"F atoms in "BF"_3BF3 and "BF"_4^-BF−4 is 226 pm, despite the longer "B-F"B-F distance in the tetrahedral structure.
(from alpha.chem.umb.edu)
It is as if the "F"F atoms are closest-packed (like in a crystal), with the "F"F atoms having a ligand radius of 113 pm.
When the "BF"_3BF3 forms a Lewis complex, the "F"F atoms remain close-packed, but the "B-F"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"B-F bonds than the longer, weaker "B-Cl"B-Cl bonds.
Hence "BF"_3BF3 is a weaker Lewis acid than "BCl"_3BCl3.