Jerram Barrs, in his book Shepherds & Sheep (which sadly doesn't appear to be in print anymore!), explains how the Holy Spirit and the Word of God relate in the New Testament. These insights are very helpful as I think this is a frequent issue today.
He sets up the issue by writing,
"How does the internal work of the Holy Spirit relate to the written Word of God, the Bible? Many Christians are guilty of setting one against the other almost as if they were mutually exclusive. One group has the Word; another group has the Spirit...
Then he answers the problem with clear references to Scripture:
"The New Testament knows nothing of such an opposition made between the Spirit and the Word...The New Testament has, in fact, as positive an attitude to the Word and the law as it has to the Spirit. Paul writes,
'Do not get drunk on wine, which leads to debauchery. Instead, be filled with the Spirit. Speak to one another with psalms, hymns and spiritual songs. Sing and make music in your heart to the Lord, always giving thanks to God the Father for everything, in the name of our Lord Jesus Christ.' (Ephesians 5:18-20)
Compare the Ephesians passage with Colossians 3:16-17:
'Let the word of Christ dwell in you richly as you teach and admonish one another with all wisdom, and as you sing psalms, hymns and spiritual songs with gratitude in your hearts to God. And whatever you do, whether in word or deed, do it all in the name of the Lord Jesus, giving thanks to the Father through him.'...
Notice how remarkably similar these two passages are. The only substantial different between them is that the one opens with the admonition 'Be filled with the Spirit,' and the other with the call to 'let the word of Christ dwell in you richly.' One commands us to meditate on and fill our hearts with the Word of Christ, the Holy Scripture, God's law; the other commands us to be filled with the Spirit. The implication from these parallel passages is that the two commands express similar thoughts. The Word of Christ, the Scripture, is to be central in our lives if we desire to please the Spirit, to be filled with the Spirit."
His comparison of the passages is spot on. He then concludes, stating,
"There is no tension in the New Testament between Word and Spirit...rather the two work in harmony. Why is this?...The simplest answer is that the Spirit himself is the author of the Word and has given his commandments there for our instruction. Therefore, if we want the Spirit's liberty, any church structures we create must be subject to the guidelines the Spirit has laid down in the written Word. The new wine of the Spirit can be contained only in the Spirit's own wineskins."
In summary, Barrs is extremely helpful in showing that we are not to put the Word against the Spirit. The Holy Spirit would not want this! Instead, he is the author of the Word and, in the mind of the Spirit-led apostle Paul, "be filled with the Spirit" is interchangeable with "let the word of Christ dwell in you". They are not at odds.
Quotes from Jerram Barrs, Shepherding & Sheep: A Biblical View of Leading & Following (Downers Grove, IL: InterVarsity Press, 1983), 27-34.
Additional Note: Can the 'word of Christ' refer to prophecy?
As an add on to the above quotes, one may object that the "word of Christ" in the text from Paul quoted above refers not mainly to the gospel or the Bible, but to the gift of prophecy, meaning that someone is given a particular word from Christ. In this way, someone may argue that "being filled with the Spirit" and letting "the word of Christ dwell in you" are interchangeable because the word of Christ refers to prophecy.
But Barrs also very convincingly addresses this, and he proves that in the NT, the idea of the "word", or the phrase "word of Christ", does not refer to the gift of prophecy. Here is his argument, backed up with convincing Scripture:
"In the New Testament we find widespread use of the expression the word of God. Often it refers to the Old Testament, the written and authoritative Word (see John 10:35; 1 Timothy 4:5). Again this background "the word of God" is then used to refer to God's revelation which proclaims Christ, the Word made flesh, and which is proclaimed by Christ (John 1:1, 14; John 17:6-8, 14, 17; Titus 2:5; 1 John 1:10; 1 John 2:14). The living and written Word are not opposed but rather express a unity and message.
Because Jesus is the Word of God, and because the Word proclaims him, Jesus refers to the authority of his own word in the same way he refers to the binding nature of the Old Testament word; for instance, 'Whoever hears my word and believes him who sent me has eternal life' (John 5:24; also see John 8:31-32). 'You have kept my word and have not denied my name' (Revelation 3:8). Consequently, the apostolic writers use the expression the word of the Lord or the word of Christ to speak of God;s revelation in Jesus' teaching and life which centers on the message of his death and resurrection. This, to these specially appointed men, is the authoritative and final Christian truth (Acts 8:25; Acts 12:23; Acts 13:44; Acts 19:10; 2 Thessalonians 3:1; 1 Timothy 6:3). As one lexicon puts it, the authoritative Christian message 'is simply ὁ λόγος [ho logos] = the 'Word,' since no misunderstanding would be possible among Christians' (see Matthew 13:20-23; Acts 17:11; 18:5). The passage in Acts 17:11 expresses in the clearest possible way the unity between the new 'word' and the Old Testament Scriptures: 'These Jews...received the word with all eagerness, examining the scriptures daily to see if these things we so' (RSV).
Because the authority of this word of Christ, the message about Christ spoken by the apostles is itself called the word of God; that is, it has the authority of Scripture (1 Thessalonians 2:13; 2 Thessalonians 2:15). This is true too of the written word of the apostles. And so the argument comes full circle, for the written New Testament is itself regarded as Scripture, the authoritative, written Word of God: 'What I am writing to you is the Lord's command' (1 Corinthians 14:37; see also 1 Timothy 5:18, where Paul quotes Deuteronomy and Luke equally as Scripture, and 2 Peter 3:2, 15-16). Gerhard Kittel writes quite properly that
'the phrases "word of God," "word of the Lord" are very common in the NT, but...they are never used of special divine directions...The reason for this obvious and remarkable fact is that after the coming of Jesus, the Word of God or the Word of the Lord has for the whole primitive Christianity a new and absolutely exclusive sense. It has become the undisputed term for the one Word of God which God has spoken, and speaks, in what has taken place in Jesus and in the message concerning it. From this time on, the erm cannot be used of any other revealing event, no matter how authentic and estimable...The primitive Christian conviction [is] that the revelation which has taken place in Jesus Christ is definitive and unique.' (Gerhard Kittle, "λέγω" in Theological Dictionary of the New Testament)."
As a result, Barrs concludes,
"We must therefore conclude that there is no ground within the New Testament for understanding the word of Christ to refer to the gift of prophecy."
So when Paul writes that we are to "be filled with the Spirit" and then interchangeably writes that we are to "let the word of Christ dwell" in us, he means that we are to meditate on, dwell on, immerse ourselves in the gospel message in the Bible. He cannot be talking about prophecy. As a result, it is biblically true that being filled with the Spirit is interchangeable with chewing on the Word of God, the Bible.
Quotes from Jerram Barrs, Shepherding & Sheep: A Biblical View of Leading & Following (Downers Grove, IL: InterVarsity Press, 1983), 78-80.