Find new roads and highways from last year

There's no "zero effort" way I'm afraid, as you have already seen you cannot rely on version numbers. A relatively stable approach could be something along these lines:

• import area of interest (as of today) into PostGIS database with osm2pgsql
• import same area (as of one year ago) with a different prefix (so that you e.g. get a table planet_osm_line with today's data and old_osm_line with that of a year ago)
• delete everything from the "new" table that is in the vicinity of something from the "old" table - one approach could be creating a buffer of, say, 20 meters around every "old" road geometry and then subtracting the resulting polygons from the "new" line geometries
• what remains in the "new" table are those bits where one year ago there was no road within 20 meters of it.

The 20 meter rule is to account for small geometry changes. Of course you could fine-tune this to e.g. count a street as "new" also if the name has changed from earlier or so.