I'm not sure you are remembering correctly. Coh 4vs 4 mostly ended in massive supertank and vetted med tank spam plus a whoop load of call ins. And dont forget the non stop arty.
4vs4 were hardly ever strategic battles. It was about who cold amass the rolling ball of doom first and smash it in your face, and polly whomp your base.
Are you sure you played US much? US does not have a "rolling ball of doom" and only seemed to if you were already losing as Axis. US/allies had to grab and hold field dominance to prevent vet-spam and panther swarms. If you ever played US you knew by mid-game if you had a chance or not. It was far FAR more exhilirating to come back from a near-defeat in mid/late game as US. As Wehr, you could be down 50-450 and by 50-400 you knew you would win, the question was just if you would have to grind it out or steamroll.
Finally the Brits might be able to get a "ball of doom" but to do so would take lots longer since their units were expensive. Also they had to have good teammates who could protect them as they set up.