Drainage-type and barrier-type EIFS look virtually identical from the outside, but you may be able differentiate them by looking under the horizontal edge of the EIFS where it comes to an end, such as at the top of a window or at the bottom of the wall close to the ground.
A drainage-type EIFS will have some sort of gap, flashing, or a perforated piece of metal or plastic trim, to route water from the drainage cavity to the outside. However, the presence of such a gap is not a foolproof indicator, as some barrier-type EIFS also incorporate this feature. Cutting through the EIFS to check for building paper between the foam and the sheathing is also not a reliable method, as some barrier-type EIFS also incorporate a paper layer. The paper alone does not produce a true drainage cavity.
Once again, it would be worthwhile to hire an experienced contractor to inspect the EIFS.