No one disputes that the Bryn Glas tunnels are a bottleneck – but there are major disagreements over what precisely needs to be done.
The Welsh government wants a completely new road through the south of Newport, costing over £1 billion. Others think it would be better to improve Newport’s southern distributor roads. The technical options for a new M4 are examined in http://www.foe.co.uk/sites/default/files/downloads/m4-blue-route-45610.pdf
In my lifetime I have seen hundreds of miles of motorways built. My subjective impression is that they do ease congestion for the first 1-2 years – but then this encourages more vehicles to the road and journey times revert.
My preference would be, if the Welsh government has $1 billion to throw around, to make a massive investment in better public transport (such as the proposed South Wales metro system) to reduce the number of cars on our roads. 
Their choice of the very expensive £1 billion road option is, naturally, preferred by the powerful roads’ lobby who have influenced the UK’s transport policy ever since the first motorway was opened in 1957. But journey times have hardly improved at all during the past half-century.
I believe it’s time for a rethink and reversion to public transport.
Dr John Cox blogs 