CISC is more restrictive and limits the C coefficients to loads acting parallel to the weld group. For inclined loads, the AISC is the way to go. Table 3-27 was primarily intended for in-plane loading. For out-of-plane loading, Table 3-34 was provided, but again is restricted for loads acting parallel to the weld group.
To comment on KootK's remark, the C coefficients are not dimensionless parameters. The C coefficents represent the equivalent weld stress resultant from a force acting at a set eccentricity from the weld group's center of gravity. They are therefore dependent on the strength of the electrode applied (AISC = 70ksi; CISC = 490MPa ~ 71ksi). You can convert AISC C coefficients to an equivalent CISC C coefficient by dividing the AISC C coefficient by 12 (this is a result of how each manual communicates the values using the weld size; the AISC which applies the weld size in the number of 1/16" the weld is comprised of (e.g. 5/16" fillet equates to 5 x 1/16, therefore D=5 for AISC method) and CISC which uses the leg size for D (e.g. 5/16" fillet is equated to a 8mm fillet, therefore D=8). The conversion factor of 12 results from 0.75 x 16 (0.75 being the phi factor, and 16 coming from the AISC weld size definition). This conversion factor does assume that the same electrode is applied across each manual, so take that into consideration if applying this conversion factor.
For out-of-plane loading using the AISC manual, you should be cautious as to its use. I believe the design tables implicitly assume that the connection material is rigid enough to develop the full weld strength. In certain framing conditions, this may not be the case. For a prime example, consider a double angle connection welded along its toes to the support (a pretty typically framing case) and subject to an axial load and a vertical shear at some eccentricity. The AISC tables may appear suitable, but research has shown the welds prematurely fail due to the angles being too flexible; additional stresses build in the welds as the angles rotate and cause bending/tension at the root of the welds. A case where the AISC tables for out-of-plane loading would be suitable would be a HSS outrigger with 2 parallel welds to the support subject to an axial load and a vertical shear at some eccentricity.