Depends on the vintage. The collectible old 15 in. Tannoys that cost a mint have a tubby mid range, limited bass and rolled-off highs, as well as limited power-handling capability. You can't mate a 15 in. woofer to a tweeter and expect a woofer of that size to produce adequate mids. And anyway, the cones are too shallow to produce a quality mid range. The smaller coned drivers(in the 10 and 12 in. range) are more cohesive in the mids, but have the same problems in the treble. And if you like excellent top-end response, you're going to have to spring for a set of those ridiculously expensive Tannoy super tweeters. I have a friend who has 4 pairs of vintage 15 in. Tannoys. He has equipped two pair with super tweeters.
Many of the newer Tannoys, around 1990 vintage and beyond, have a much steeper angle to the cone that flares out nicely, allowing much better reproduction of the mids. The newer treble drivers are also much better than those of 40 years ago, no super tweeters needed. Tannoy products of today might look similar to yesterday's versions, as is indeed the case with the Westminster and the Churchill. But due to improvements in manufacturing, technology and materials, they are a different animal than their predecessors. I've had several pairs of Tannoys, so I've had a chance to compare different genres. The above comments are based on those observations. I once bought a pair of 1970's vintage Tannoys for cheap and thought I had the bargain of the century. I took them home and compared them to a pair of 1991 Tannoys. There was no comparison. The vintage Tannoys were out the door a few weeks later.