Matajur probably pleases everyone. The top is relatively easily accessible and the descent is long up to 10km finishing way down in Špeter village in Italy. Yes, the Soča Valley offers some amazing transboundary trails which take you across Slovenian border to the Italian side. Since there are no actual borders any more it feels very natural to explore all the area in our surroundings. Here is a Matajur South trail form the Soča Valley Guide Book in German language - PDF.
1300m of altitude difference, 10km of ascent, 13% of average slope, with 20% steepness on the very beginning of ascent just outside Zatolmin - these are some facts that make this way up to Sleme not very popular among mountain bike riders to say the least. But there are some who like it just for these facts. The way up takes some effort but when you get to the top where the highest mountain pasture of Tolmins region lies the view opens to the Julian alps on the East and West side. From here many possibilities for descent are available. The most popular is to go down to Mederje and via Pretovč straight down to Zatolmin. The single track is always empty and it allows a very high speed descent with some rocky sections just to keep the thing interesting.