John Ker wrote:
..a compact camera to take with him when he goes mountain biking. He wants the photos to have quality worthy of being used in a magazine. He shoots photos for magazines occasionally, both with his phone and with a Canon Rebel digital camera, but he doesn't want to take a DSLR with him on his rides. Can anyone recommend a high-quality, compact camera with good image quality and good autofocus performance for him to use?
All the previous responses have talked about compact cameras, mostly concerned about size and weight, with some bringing up other factors like cost.
No one appears to have addressed the fact that the buyer plans to use this camera to make "magazine quality" images and that "he or she shoots for magazines occasionally".
Even now, we don't know WHICH magazines or have any idea WHAT he shoots. Landscapes? Wildlife? Mountain biking? Flowers? Is he paid for this work?
We can only work with the info we have...
To me "magazine quality" means as large a sensor as possible, which is not the case with many of the compact point n shoots, bridge cameras and especially phones. Image quality and resolution are one reason bigger is better when it comes to the sensor, but there also is effect on depth of field and the usable ISO range.
Obviously a full frame camera would not be a good choice due to size and weight. Maybe a step down to APS-C (1.5X or 1.6X) is more "doable"? Unfortunately both formats offer very few viable non-interchangeable lens cameras. In fact, all full frame models use a fixed prime lens, usually a wide angle (28mm or 35mm). The same is true of most APS-C point n shoots. There's exactly one APS-C with a zoom... Canon G1X Mark III. And it's limited to approx. 24-72mm full frame equivalent. If you take another step down in sensor size to Micro 4/3 (2X) you will find Leica and Panasonic models with zooms, but once again limited to a modest 24-75mm full frame equiv. range.
Looking for quality for publication I would really be reluctant to go to 1" (2.6X) or smaller. I definitely wouldn't want to depend upon 1/2.3" (5.5X) sensor cameras, which are the bulk of the point n shoots on the market and especially bridge cameras with wide ranging zooms. More info about image sensors:
https://en.wikipedia.org/wiki/Image_sensor_formatBecause of all this, there might be an alternative worth consideration. But first let's consider the DSLR the buyer already has. We only know it's a Canon Rebel. The lightest DSLR of all is the Rebel SL3 that weighs about 1.5 lb. with 18-55mm kit lens. Most other Canon Rebels will come in closer to 1.75 or 2 lb. fitted with 18-55mm kit lens.
Here is a summary of non-interchangeable lens cameras, some of which have been mentioned:
Panasonic ZS200..... 12 oz. (0.75 lb.), 1" sensor, 24-360mm equiv., $598
Canon G7X Mk III.... 14 oz. (0.87 lb.), 1" sensor, 24-100mm equiv., $700
Panasonic FZ-1000... 1.8 lb., 20MP 1" sensor, 24-400mm equiv., $848
Panasonic LX100 II.. 12.3 oz. (0.76 lb.), 17MP Micro 4/3 sensor, 24-75mm equiv., $997
Canon G1X Mk III.... 14 oz. (0.87 lb.), 24MP APS-C sensor, 24-72mm equiv., $999
Sony RX100 IV......... 11 oz. (0.69 lb.), 20MP 1" sensor, 24-200mm equiv., $1298
Leica D-Lux IV......... 14 oz. (0.87 lb.), 17MP Micro 4/3 sensor, 24-75mm equiv., $1395
Sony RX10 IV.......... 38.5 oz. (2.41 lb.), 20MP 1" sensor, 24-600mm equiv., $1698
I didn't forget Nikon... they just don't make any point n shoots with larger than 1/2.3" sensor.
I didn't include the Oly TG-6 because that 9 oz. camera with a 25-100mm equiv. zoom also uses a 1/2.3" sensor (12MP).
Now for something shocking. Some interchangeable lens cameras are close to the same weight as some of those compacts. Sometimes even lighter!
Canon R50, 24MP APS-C mirrorless w/RF-S 18-45mm & RF-S 55-210mm lenses... 1.5 lb., $1029.
Canon R10, 24MP APS-C mirrorless w/RF-S 18-45mm & RF-S 55-210mm lenses... 1.9 lb., $1348
(18-45mm lens full frame equiv. is 29 to 72mm...... 55-210mm lens FF equiv. is 88 to 336mm.)
If you don't need that much telephoto reach, a single RF-S 18-150mm lens (equiv. to 29 to 240mm on full frame) weighs a little less than the two lenses.
Canon R50 with 18-150mm, 1.5 lb., $1178... Or R10 with 18-150mm, 1.63 lb., $1279.
With these mirrorless, in addition to light weight and competitive price, you get some of the most advanced autofocus available. And have the versatility to add lenses later, if wanted. An APS-C size sensor is not quite as good as full frame at high ISO or when it comes to depth of field control, but APS-C will be better than the smaller size sensors used in many point n shoots. Some of the point n shoots listed above top out at 1/2000 shutter speed... while these two have 1/4000. Frame rates vary, but at full resolution none of the compacts match the R50's 15 fps electronic shutter. It has no mechanical shutter, instead has a 1st curtain electronic where its frame rate drops to 12 fps. The R10 is even faster at 23 fps with its electronic shutter, 15 fps with its mechanical. Both have articulated rear Touchscreen LCDs. Both have small built-in flash, as well as hot shoes for external flash. (Note: R50 uses a unique flash shoe that Canon has been putting on their more entry level cameras lately... there is a limited selection of flashes than can be used directly in it, but there also is an adapter to allow standard flash to be used.) Neither of these models have IBIS, but most lenses for them have IS that can provide up to 5 stops worth of assistance.
In other words, an R10 or the new R50 with select lenses would not only able to outperform most of the point n shoots... bigger sensor, better image quality, more control of depth of field, higher usable ISO, better AF, versatility.... there is little weight penalty, in some cases a mirrorless with it's lenses actually can weigh less... they also can be competitive in price with the more advanced point n shoot and bridge cameras.
Both Nikon and Sony offer APS-C mirrorless may be worth consideration, too. I just focused on the Canon system since that's what I'm most familiar with.
Finally, depending upon exactly which camera and lens(es) they have, the would-be buyer's current Rebel kit actually might already be lighter than some of those bridge cameras!