Answer: Clay soil in and of itself is not a bad thing, but some shrubs are suited to clay soil better than others. If you have planted shrubs that prefer an organic, humusy soil or a very well drained soil then they may not be happy growing in clay.
You might also find that they have failed to root outward beyond the original planting hole. This can happen if there are encircling roots that are not cut or unwound and directed outward at planting time, or if the sides of the planting hole are very slick and smooth, or if the planting hole was not dug wide enough with soil loosened over an area several feet across to encourage rooting.
In my experience, water is probably the most limiting factor in plant growth. If the soil is similar and they were planted the same way, but the one receiving more water is doing better, then I would tend to think you may need to water the other more heavily to make it grow equally well.
Clay soil is special in that it will hold moisture longer than a faster draining soil, but once it dries out it requires special care to re-wet it. Clay soil must be watered very slowly and for a long time to rehydrate it. To check you watering, dig into the soil with your finger. If it is still damp you do not need to water yet. When you do water, water slowly and deeply so it soaks down deep. Wait about twelve hours after watering and then dig down to see how far the water soaked in; sometimes it can be surprising. I hope this helps you trouble shoot.
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