Question

Any method is just an estimate.

I looked into which methods were most likely to be closest to accurate for exercises I do regularly.

For bike or rowing machine, the watts-based estimate (if it has one) is more likely to be accurate (though the machine's estimate may ideally need to be converted from gross to net calories (i.e. estimated BMR/RMR subtracted).

Heart rate monitors may be somewhat accurate for moderate steady state cardio, for someone with a HRmax that's close to age-estimated values (220-age, generally - but many people have a non-average HRmax) or when the HR monitor knows their tested/measured HRmax. The further the exercise type is from moderate steady state cardio, the more iffy the estimate gets, and it's likely to be very questionable for something like HIIT, intervals generally, or strength training.

For walking, I usually use the ExRx walking calculator, with the "energy" box set to "net".

https://exrx.net/Calculators/WalkRunMETs

Strength training is especially hard to estimate. These days, some fitness trackers use a METS-based estimate (same methodology the MFP cardiovascular exercise database uses) rather than a HR estimate. I use the MFP cardiovascular exercise database "Strength training" entry for lifting. It's not going to yield a large estimate.

In general, I try to be as accurate as I can, but exercise estimates are approximate - fortunately, usually one can get close enough to be useful, in a real-world context. Faced with multiple sources of calorie estimate, and with no info about which is likely to be best-founded, I'd tend to pick the lower estimate, personally. YMMV.

Current methods are:
Power meter for cycling.
MFP database entry for strength training (log entire duration).
Online calculator linked above for long walks.

When I started out I used a HRM for cardio (please don't use it for strength training as that's not an aerobic exercise!) and at the time my heart rate and exercise heart rate were a bit lower than average. Estimates for steady state were reasonable enough for purpose to be useable. But those estimates were gross calories and not net calorie estimates which are better to use.
Some estimates from gym cardio equipment were a bit high in retrospect but still good enough for purpose - it takes a lot of hundreds of exercise inaccuracy to impact the thousands of weight loss and of course using consistency and making adjustments to your calorie balance works well.

When I started to use a stationary bike with power meter I could fine tune my settings on my Polar HRM to get to a decent level of accuracy for steady state. But that accuracy falls apart for hard intervals on the bike or simply getting very hot.

I still wear a HRM for cycling but only for what they are really good at, measuring your heart rate.

Your personal exercise selection determines which methods work well - what are you doing?

I use an Apple Watch for all exercise types, including strength training. I have a few years of data logged including weight, exercise, and calorie intake as well as periodic metabolic testing under my belt, so I know exactly where to set my base calories to meet my goals. I usually eat back close to 100% of my exercise calories. This doesn’t work for everyone- it’s highly individual. In my experience the best thing to do is pick a method and try it for a month or two, then evaluate and tweak as needed based on the results.

Both numbers are just estimates. I will also say that HRM are good for knowing what your heart rate is...but not necessarily super accurate for calorie burn particularly the more intense the workout was.

Anecdotally - when I got back into running I used a Polar HRM with a chest strap. I'd wear that during my run, and I'd also use my running app (both methods also knew my height/weight/sex, etc.). I noticed on my more strenuous runs (i.e. faster pace, included elevation changes, etc.....higher avg. HR for the duration of the exercise, or if it was really up/down like I was doing intervals)....the higher the calorie burn estimate was from my HRM. It would sometimes be even 100-150 calories higher than my running app estimate. I ended up choosing a number between the two and manually putting that into MFP. I lost weight at the expected rate so...seems the answer was somewhere in the middle. Their estimates would be more/less the same when I was walking/hiking/when HR was lower and more consistent.

Just my 2c. Nothing is going to be exact - just choose a number that seems as best as you can figure. You can even look up a couple sources for calories burned on the internet - including looking up calories burned by avg. HR if you like. Average all that info and use that number, should (theoretically) be closer than any one estimate.

The calories burned that MFP automatically gives you can be accurate or really far off. So I almost never use those. Now that I'm in maintenance and not really logging anything, I really just take a peak at the calories burned on my running app when I'm done with a run just so I know a ballpark number of what I need to eat....although I'm pretty good now at just paying attention to my own hunger cues/energy levels.