Any scissor you purchase should have uniform hollow-grinding (CONCAVE) on the inner surface of the blade and a narrow but consistent “ride line” along the cutting edge.

In general, most poor quality scissors (made out of poorer quality steels such as 400 and 420 stainless steels) have a beveled edge because this edge is thicker than a convex edge and this thickness helps support the sharp edge of the blade.  This means that the scissor will never cut as well as a convex shear and the edge will deteriorate more quickly.  However, there are some older brands of Japanese scissors such as Omega, Nova, Fuji, Matsuzaki, etc. that have been engineered for a very sharp bevel edge made out of fine quality Japanese steels that will perform every bit as well as a quality convex edge.  Most shears are made with a convex edge now because stylists have been told that convex edges are better and so it is easier to go with the flow.  And since the quality of a beveled shear must be VERY high to equal the performance of a convex shear, convex edges are more advantageous in the mid-range to lower-range shears.

Most stylists prefer a CONVEX (Hamatguri or Clamshell) edge.  However, if the steel in your shear is of superior quality and the blade was designed originally with a beveled edge, that is the edge it should always have.