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.