I am wondering about the root area.  On the left there is clearly stone near the root line.  Stone and rocks can absorb heat and keep the root area warmer hence an earlier soil warmup.  While we don’t recommend putting anything but mulch in the tree’s dripline because it can decrease available moisture, the stone may have a soil warming effect.

I can’t see the root base for the tree on the right.  If the buds are green, it is still alive.  There isn’t anything that can be done to speed up the process at this point.  If it is not mulched, you could try mulching it for next year.  It may have something to do with an extremely dry spring but the latest rains should have solved that issue. 

It’s interesting that two identical trees should have such a different leaf out time. Is there any possibility that lawn care chemicals/herbicides may have been used near the tree on the right creating an additional stressor?

Check for any disease process that could cause stress as it leafs out.  See the website for possibilities:  http://apps.extension.umn.edu/garden/diagnose/plant/deciduous/birch/

Hi Mary, thanks for your help.

Attached is the picture of the ground. The other side of the fence is just neighbor's lawn. This patio has been here the entire time the trees have been planted.

The buds are green when broken open, but they seem to be wimpy. Dont show signs of swelling and impending leaf out.

We did apply Tenacity for weed control, the whole lawn got it, not just a specific area. Our application rate was 1 teaspoon in 1 gallon of water applied to about 1500 sqft of turf. I also put down some starter fertilizer for grass seed we put down.
Tenacity Herbicide | Greencast | Syngenta (greencastonline.com)

I guess time will tell. If you have any other thoughts, I appreciate learning from an expert.

Thanks again,

That herbicide is unlikely to cause problems with these trees.  I do recommend that you mulch the trees for a couple of reasons. 

First, grass outcompetes trees for moisture and nutrients. Second, although your brick pavers appear to be permeable letting water into the root system, it would not be at the same rate as if there were no pavers. Did you by any chance put plastic under the pavers?  If so that would restrict the water available to the trees. The majority of tree roots are in the 8” just below the surface.  I cannot see the root flare..where the roots come out from the tree trunk. It may be hidden in the grass.  If you can’t see the root flare, it is planted too deep. This is Another reason to pull back the grass and expose the root flare and put down mulch.

For now water the trees regularly if no rainfall. Mulching is recommended for trees, especially in lawns.  In this situation it may make the difference between healthy and struggling trees.

You are welcome.  When mulching, the mulch should not touch the bark...leave 4-6”.  Mulch touching  bark can harbor pests.  See:  https://extension.umn.edu/planting-and-growing-guides/watering-newly-planted-trees-and-shrubs