The majority of billboard trees do not present any performance issues due to the small sizes of their meshes and low quality textures. However where they do present problems, particularly when used in large numbers, is in their lack of LODs and their "unrealistic" appearances. The lack of LODs can be an issue if a route has a large number of them in the far distance - each one has to be rendered in full and then reduced to a few pixels in size (a problem common to all assets that do not have LOD data). The worst offenders by far are billboard tree splines - worst assets ever created in my opinion. Billboard trees used wisely should not present any issues.
I cannot recall ever having any performance issues using SpeedTrees. But, like anything, it can depend on your system and performance settings. If you max everything out on a high detail route you can run into problems even on a high performance machine.
SpeedTrees have been a highly successful replacement for billboard trees and bushes for some time now but they have started to show their age and you must buy a license to be able to create them. Thankfully, last year N3V started using a free replacement for SpeedTrees in PlantFactory trees and bushes. These use LOD data and a new feature (new for Trainz but not for other games) called "Imposters" which render distant 3D trees as 2D surfaces that always face the camera. There is a growing number of PlantFactory assets on the DLS and I have replaced most of my SpeedTrees with PlantFactory equivalents.
One route that I encountered a few months ago, <kuid2:214658:101010:1> Aylesbury to London Marylebone (Updated), was a mass of billboard trees and tree splines used everywhere in great numbers. Surprisingly it still ran reasonably well in TRS22 SP6 HF1 but there were rendering issues for distant objects - mostly billboard trees and tree splines. I did some major surgery on the route and deleted all the tree splines and replaced all the billboard trees and bushes with PlantFactory alternatives. There was a significant improvement in performance and the rendering issues disappeared.
But that was my experience. Others may have had different results on different systems.