In my kind of on-going journey away from dispensationalism, I've come to see where there is at least a subtle difference. A covenantal view emphasizes God's work throughout history in redeeming a people for Himself and for His glory. It also sees Christ reigning right now as opposed to an exclusively, or practically exclusively, future reign in a Jewish millennial kingdom. In dispensationalism, the purpose of God's kingdom, in the future, is primarily to fulfill His promises to the nation of Israel. In covenantalism, the purpose of God's kingdom, now and in the future, is to display His glory to and through His people.
With these different perspectives, I think covenantalism puts more emphasis on living out the implications of the gospel in every realm of life, in order to display God's glory and power in this present world. Dispensationalists often focus on simply "winning souls" who will be blessed in a future kingdom. I see the covenantal approach as being more "holistic" in respect to the application of the truths of the gospel.
These distinctions apply more directly to full-orbed, traditional dispensationalism. The progressives have made a definite shift toward recognizing the presence of the kingdom of God in the church in this age. The last chapter of "Progressive Dispensationalism" by Blaising and Bock touches on the social implications of their view of the kingdom as having been inaugurated in Christ.
My perspective on it anyway.

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Mike Shingler
Pastor: Steep Hollow Baptist Church (SBC)
Bryan, TX