Left: Bumped specular built-in shader

Right: Specular built-in shader

What I don't understand is why the right one has a "less-detailed" specular highlight. It almost looks vertex-lit. This is being a problem, because I'm using a shader that's using the type of specular highlight on the right. I want it to look like the one on the left. Can I just integrate bumpmaps in to the shader? How would I do that? Asdf.

The shader I'm using:

Shader "Example/RimWorldRefl" {
    Properties {  

      _MainTex ("Texture", 2D) = "white" {}  
      _Cube ("Cubemap", CUBE) = "" {}
      _RimPower ("Rim Power", Range(0.5,8.0)) = 3.0
      _Color ("Main Color", Color) = (1,0.5,0.5,1)


    }  
    SubShader {  

      Tags { "RenderType" = "Opaque" }  
      CGPROGRAM  

      #pragma surface surf SimpleSpecular

      half4 LightingSimpleSpecular (SurfaceOutput s, half3 lightDir, half3 viewDir, half atten) {
          half3 h = normalize (lightDir + viewDir);

          half diff = max (0, dot (s.Normal, lightDir));

          float nh = max (0, dot (s.Normal, h));
          float spec = pow (nh, 250.0);

          half4 c;
          c.rgb = (s.Albedo * _LightColor0.rgb * diff + _LightColor0.rgb * spec) * (atten * 2);
          c.a = s.Alpha;
          return c;
      }


      struct Input {  
          float2 uv_MainTex;  
          float3 worldRefl;
          float3 viewDir;
      };  
      sampler2D _MainTex;  
      samplerCUBE _Cube;
      float4 _Color;
      float _RimPower;
      void surf (Input IN, inout SurfaceOutput o) {  
          o.Albedo = tex2D (_MainTex, IN.uv_MainTex).rgb * 1;
          half rim = 1 - saturate(dot (normalize(IN.viewDir), o.Normal));
          o.Emission = texCUBE (_Cube, IN.worldRefl).rgb * pow(rim,_RimPower) * _Color.rgb;
      }  
      ENDCG  
    }   
    Fallback "Specular"  
}

Help, please. D: