I think there can't be a single query to do two type of operation but there could be two queries

db.db_users.update({'device_type':"Android"},{$set : {'version':"1.0"}},{multi:true});
db.db_users.update({'device_type':""},{$set : {'version':""}},{multi:true});

also in the document it shows a blank space " ", whereas in question you mentioned it "". if it's not consistent you should user $or.

It can also be done through a single script

db.db_users.find().forEach(function(doc){if(doc.device_type && doc.device_type==='Android'){doc.version="1.0"}else{doc.version=""} db.db_users.save(doc)});

if there are multiple logic, it's better to go for script, if it's just limited as you mentioned in your question two updates would be preferable.

For MongoDB 3.4 and newer:

Using the aggregation framework, the $addFields and $out pipeline would update your collection with a single aggregate operation. For example:

db.users.aggregate([
    {
        "$addFields": {
            "version": {
                "$switch": {
                    "branches": [
                        { "case": { "$eq": ["$device_type", "Android"] }, "then": "1.0" },
                        { "case": { "$eq": ["$device_type", " "] }, "then": "" }
                    ]
                }
            }
        }
    },
    { "$out": "users" }
])

For MongoDB 3.2:

You could utilise the bulkWrite methods for faster and more efficient updates. Consider the following operation:

var ops = [];
db.users.aggregate([
    {
        "$project": {
            "version": {
                "$cond": [
                    { "$eq": ["$device_type", "Android"] },
                    "1.0",
                    ""
                ]
            }
        }
    }
]).forEach(function(doc){
    ops.push( { 
        "updateOne": {
            "filter": { "_id": doc._id },
            "update": { "$set": { "version": doc.version } }
        }
    });
    if (ops.length === 500) {
        // Execute per 500 operations and re-initialise
        db.users.bulkWrite(ops);
        ops = [];
    }
})

if (ops.length > 0) {
     db.users.bulkWrite(ops);
}

For MongoDB <= 3.0 and >= 2.6:

var bulk = db.users.initializeUnorderedBulkOp();
var count = 0;

db.users.aggregate([
    {
        "$project": {
            "version": {
                "$cond": [
                    { "$eq": ["$device_type", "Android"] },
                    "1.0",
                    ""
                ]
            }
        }
    }
]).forEach(function(doc) { 
    bulk.find({ "_id": doc._id }).updateOne({ "$set": { "version": doc.version } });
    count++;
    if (count % 500 === 0) {
        // Excecute per 500 operations and re-initialise
        bulk.execute();
        bulk = db.users.initializeUnorderedBulkOp();
    }
})

// clean up remaining operations in queue
if (count > 0) {
    bulk.execute();
}