Depends on your idea of messy! Although, I think honeysuckle tends to be messy by any standards. It is best in a shrub or tree in a wild area of garden.

Most important is to consider orientation. Jasmine will need a sheltered South-facing fence, in a mild part of the country. Honeysuckle will tolerate less sun, but it is messy, and does flower better with sunlight.

I would recommend clematis armandii - it is evergreen, and a bit tidier, but does have scented flowers, some selections are better ('apple blossom' I think). It will also tolerate a less sunny situation, provided its not too cold or exposed.

Trechelospermum Jasminoides is a very attractive neat evergreen climbing shrub with small scented flowers. It does need a warm site with plenty of sun, though.