Hidden roof gutter or Lead flashing

I've had some quotes for re-roofing a very old 1906 terraced house in Manchester.

One roofer told me that they don't make these tiles any more( old Belgian tiles he said they are called) so he suggested to join the old tiles of the neighbour with my new tiles using a hidden underneath gutter that runs all the way between the joint of the new and the existing next door tiles.

With regards to waterproofing is this a better option or shall I go with what most other roofers have done on the same street, that is using lead to bridge the different type of tiles.

He will be using new double roman tiles.

Thanks...

If i've got you right, they will be using Bonding gutters, these fit under next doors tile and under your new tiles as well, there made off fibeglass and look like a flat fiberglass valley.
They are a much better design idea than just the lead just covering the joint.
Hope this helps
Dave