That little difference becomes very important in road cycling... I personally always recommend used road bikes. New, you have to spend many thousands. But I've seen superb used options (e.g. carbonfiber, ultegra or nowadays even 105, decent wheels and handlebars) for under 1000€.

One will have to spend a little extra to replace a couple parts, but it's still a fraction of the new cost. My first good road bike was third hand and I was cycling competitively.

A bike just for weight loss or something similar can be cheaper, of coarse. But serious road cycling is often trickier, you'll want carbon fiber at least. YMMV though