My preference on 24-megapixel Nikon is generally to crop at the computer. On APS-C, which I used from 2001 to 2006, was to use a tele-converter. At that time, I had APS-C cameras of 2.7 MP, 6MP, 8.2 MP, and then 12.2 MP, and on APS-C both the lens and the converter were not "seeing" the weakest part of the lens or converter: the edges of the lens's field and the edges of the converter's field.
Tele-converters are ALWAYS a bit of a compromise. Some tele-converters are well-matched to specific lenses, some are average, some are very poor matches to specific lenses. The old so-called "matched converters" which were actually designed to be used with a specific lens, made their appearance in the mid-1970's for zoom lenses, and Nikon made some converters that worked very well with specific long tele lenses, beginning at 300mm, with the TC-300 and TC-301 models for lenses 300mm and longer, and later had the AF-i converters which were designed for the then small handful of super-tele, AF-i focusing, big glass lenses (which was a VERY small group of high-grade lenses). Today, Canon has really awesome converters for their new 70-200 Mk 11 f/2.8 zoom, and today, Nikon has $500 converters with aspherical element designs, and which work pretty well on their big glass lenses and the 70-200 mark two.
The way it works is this: each person needs to decide if a particular converter paired with a particular lens is good enough for specific uses. A really good wildlife blogger went through the various Nikon AF converters he has, with specific Nikon lenses like 200/2 VR, 300/2.8 VR, 400/2.8, and so on. For some uses, he was satisfied that the TC unit was acceptable. Birding often has a bird in the central area of a frame, with an indistinct sky or water background, and many good bird shots have been made with a long lens and a TC. Long-distance landscape work might not look nearly so good if the corners show bad image quality. As 480sparky said, "It depends".
But simply, consider this: a converter brings with it optical lowering of image quality. If the main lens is a good lens, and you have a high-megapixel image, it ought to crop reasonably well and still hold up. Now that most people have 20 MP, I think converters make less sense than they did back in the 2.7 to 8 MP era.