In an ideal world I would suggest both as they fit different purposes, but if you really have to decide on one or the other I have compiled a list of their respective benefits.
Cold Frame Cloche
  • Permanent / Semi Permanent
  • Ventilation adjutable
  • More Expensive
  • More Robust
  • Moveable
  • No Ventilation Adjustment
  • Cheaper
  • Less Robust

The cold frame's fixed location and adjustable ventilation make it ideal for hardening off plants that have come from either the greenhouse or indoors. The ability to progressively open the roof light more each day allow a gradual acclimatisation. Also wooden cold frames in particular are better a retaining heat during the night.

Cold frames tend to be of a more solid construction and heavier meaning that they are more resilliant to wind and other damaging factors. However their increased weight and permament nature means that they are exposed to the worst of the weather whereas a cloche can be brought indoors. Also as a cloche is moveable it can be moved to different areas of the garden as the need arises.

Finally, cloches are generally cheaper, particularly polythene tunnel cloches. Although the polythene on these cloches tends to deteriorate over time they can be an inexpensive way to get large swathes of you garden off to an early start.

In summary, if you want to extend the growing season and harden off seedlings then buy a cold frame. However if you want something to aid germination directly in your garden, then a cloche is probably the answer.