Well, I have both, a 6’/8′ greenhouse I bought from Harbour Freight and a self-made 8’/9′ high tunnel made with welded wire/cattle panels. It probably really depends on the quality of the greenhouse you buy, but my little greenhouse is not as tight as the high tunnel. Granted, in the summer the high tunnel gets hotter because of its positioning to the prevailing winds to air it out, but, like mentioned before, the greenhouse seems to cool out much quicker. In winter, I only store cold hardy plants in there that I just want to get out of the harsh/freezing winds.
Some time/month ago, I watched a video in which they showed a high tunnel where the owner constructed a second layer as an added barrier for warmth, sort of an air pocket for additional insulation (a high tunnel within a high tunnel), maybe that’s something you want to consider.
good luck 👍