Because you happen to have exact format of the field every time (circle is a two element array) you can transform it in aggregation framework into two fields and then compare them in a projection, and match to get back just the elements satisfying your requirement of second array element being greater than first array element.
db.place.aggregate( [
{ $unwind : "$center" },
{ $group : { _id : "$_id",
centerX : {$first:"$center"},
centerY : {$last:"$center"}
} },
{ $project : { YgtX : { $gt : [ "$centerY", "$centerX" ] } } },
{ $match : { YgtX : true } }
] );
Now, if your array was an arbitrary pair of numerical values, then you can use the above.
You said in comments that your pair represented coordinates (lat, long) - keep in mind that in MongoDB coordinate pairs are always stored as long, lat - if your actual x, y values were coordinates in on a flat (as opposed to spherical) place, you could find all the documents that had Y coordinate greater than X coordinate with a single geospatial query:
db.place.find( { center : { $geoWithin : { $geometry : {
type:"Polygon",
coordinates:[[[50,50],[-50,50],[-50,-50],[50,50]]]
} } } } );
The above query assumes that your coordinate system goes from -50 to 50 along X and Y and it finds all points in the triangle that represents all coordinates having Y >= X.