#Java 7, (削除) 112 (削除ここまで) 104 bytes

int c(int[]a){int i=a[0],j;for(int b:a)i=(j=(i+"").length()-(b+"").length())>0?b:b>i&j==0?b:i;return i;}

Different approach to save multiple bytes thanks to @Barteks2x.

Ungolfed & test cases:

Try it here.

class M{
 static int c(int[] a){
 int i = a[0],
 j;
 for(int b : a){
 i = (j = (i+"").length() - (b+"").length()) > 0
 ? b
 : b > i & j == 0
 ? b
 : i;
 }
 return i;
 }
 public static void main(String[] a){
 System.out.println(c(new int[]{ 1 }));
 System.out.println(c(new int[]{ 9 }));
 System.out.println(c(new int[]{ 1729 }));
 System.out.println(c(new int[]{ 1, 1 }));
 System.out.println(c(new int[]{ 34, 3 }));
 System.out.println(c(new int[]{ 409, 12, 13 }));
 System.out.println(c(new int[]{ 11, 11, 11, 1 }));
 System.out.println(c(new int[]{ 11, 11, 11, 11 }));
 System.out.println(c(new int[]{ 78, 99, 620, 1 }));
 System.out.println(c(new int[]{ 78, 99, 620, 100 }));
 System.out.println(c(new int[]{ 1, 5, 9, 12, 63, 102 }));
 System.out.println(c(new int[]{ 3451, 29820, 2983, 1223, 1337 }));
 System.out.println(c(new int[]{ 738, 2383, 281, 938, 212, 1010 }));
 }
}

Output:

1
9
1729
1
3
13
1
11
1
99
9
3451
938

Java 7, (削除) 112 (削除ここまで) 104 bytes

int c(int[]a){int i=a[0],j;for(int b:a)i=(j=(i+"").length()-(b+"").length())>0?b:b>i&j==0?b:i;return i;}

Different approach to save multiple bytes thanks to @Barteks2x.

Ungolfed & test cases:

Try it here.

class M{
 static int c(int[] a){
 int i = a[0],
 j;
 for(int b : a){
 i = (j = (i+"").length() - (b+"").length()) > 0
 ? b
 : b > i & j == 0
 ? b
 : i;
 }
 return i;
 }
 public static void main(String[] a){
 System.out.println(c(new int[]{ 1 }));
 System.out.println(c(new int[]{ 9 }));
 System.out.println(c(new int[]{ 1729 }));
 System.out.println(c(new int[]{ 1, 1 }));
 System.out.println(c(new int[]{ 34, 3 }));
 System.out.println(c(new int[]{ 409, 12, 13 }));
 System.out.println(c(new int[]{ 11, 11, 11, 1 }));
 System.out.println(c(new int[]{ 11, 11, 11, 11 }));
 System.out.println(c(new int[]{ 78, 99, 620, 1 }));
 System.out.println(c(new int[]{ 78, 99, 620, 100 }));
 System.out.println(c(new int[]{ 1, 5, 9, 12, 63, 102 }));
 System.out.println(c(new int[]{ 3451, 29820, 2983, 1223, 1337 }));
 System.out.println(c(new int[]{ 738, 2383, 281, 938, 212, 1010 }));
 }
}

Output:

1
9
1729
1
3
13
1
11
1
99
9
3451
938

#Java 7, 112 bytes

int c(int[]a){int i=a[0];for(int b:a)i=b<i?b:i;for(int b:a)i=(i+"").length()==(b+"").length()&b>i?b:i;return i;}

Ungolfed & test cases:

Try it here.

class M{
 static int c(int[] a){
 int i = a[0];
 for(int b : a){
 i = b < i
  ? b
 : i;
 }
 for(int b : a){
  i = (i+"").length() == (b+"").length() & b > i
 ? b
 : i;
 }
 return i;
 }
 public static void main(String[] a){
 System.out.println(c(new int[]{ 1 }));
 System.out.println(c(new int[]{ 9 }));
 System.out.println(c(new int[]{ 1729 }));
 System.out.println(c(new int[]{ 1, 1 }));
 System.out.println(c(new int[]{ 34, 3 }));
 System.out.println(c(new int[]{ 409, 12, 13 }));
 System.out.println(c(new int[]{ 11, 11, 11, 1 }));
 System.out.println(c(new int[]{ 11, 11, 11, 11 }));
 System.out.println(c(new int[]{ 78, 99, 620, 1 }));
 System.out.println(c(new int[]{ 78, 99, 620, 100 }));
 System.out.println(c(new int[]{ 1, 5, 9, 12, 63, 102 }));
 System.out.println(c(new int[]{ 3451, 29820, 2983, 1223, 1337 }));
 System.out.println(c(new int[]{ 738, 2383, 281, 938, 212, 1010 }));
 }
}

#Java 7, (削除) 112 (削除ここまで) 104 bytes

int c(int[]a){int i=a[0],j;for(int b:a)i=(j=(i+"").length()-(b+"").length())>0?b:b>i&j==0?b:i;return i;}

Different approach to save multiple bytes thanks to @Barteks2x.

Ungolfed & test cases:

Try it here.

class M{
 static int c(int[] a){
 int i = a[0],
 j;
 for(int b : a){
 i = (j = (i+"").length() - (b+"").length()) > 0
 ? b
 : b > i & j == 0
 ? b
 : i;
 }
 return i;
 }
 public static void main(String[] a){
 System.out.println(c(new int[]{ 1 }));
 System.out.println(c(new int[]{ 9 }));
 System.out.println(c(new int[]{ 1729 }));
 System.out.println(c(new int[]{ 1, 1 }));
 System.out.println(c(new int[]{ 34, 3 }));
 System.out.println(c(new int[]{ 409, 12, 13 }));
 System.out.println(c(new int[]{ 11, 11, 11, 1 }));
 System.out.println(c(new int[]{ 11, 11, 11, 11 }));
 System.out.println(c(new int[]{ 78, 99, 620, 1 }));
 System.out.println(c(new int[]{ 78, 99, 620, 100 }));
 System.out.println(c(new int[]{ 1, 5, 9, 12, 63, 102 }));
 System.out.println(c(new int[]{ 3451, 29820, 2983, 1223, 1337 }));
 System.out.println(c(new int[]{ 738, 2383, 281, 938, 212, 1010 }));
 }
}