Best amp for Dynaudio Confidence 1 or Contour 1.4?

Both are great choices. I have owned S1.4 on two different occassions and was well served by solid state McCormack DNA-125 and Unison Research Unico SE at 140 wpc. Both provide excellent current at both 8ohm and 4ohm. Get a good power cord for your amp or integrated if you go that route.

You want something with high current. I have an Octave V70SE for my C1's. Naim is another good choice.

The dynaudios seem to like a decent amount of power, they are not particularly efficient. I used a musical fidelity M3 nuvista at 275 watts into 8 ohms with 1.3 mkIIs which are only sightly more efficient then either the C1 or 1.4s and it sounded great, but was really more power then needed.

I second Miker's suggestion. IMO Musical Fidelity and Dynaudio is a very good combination. I have tried the S1.4 speakers with quite a few amps (at the same time in the same room), e.g. NAD M3, Marantz PM-15, Cyrus separates, Primare, and Musical Fidelity A5 and X series separates. To me the combination with the Musical Fidelity amps was by far the best, i.e. very well balanced with good detail and bass and a very full midrange. The A5 amp will probably do a good job also when driving the C1s, but the C1s deserve better. The NuVista M3 amp suggested by Miker should do a great job.

I have a Parasound A21 driving Dynaudio S1.4 and it sounds very good.