Yes. Although it feels tough when you have some fatigue in your legs the computer suggests you're not working that hard and can dig deeper. It also suggests when you're overdoing it on a recovery day and should back off. Changes in resting heart rate can suggest over-training.

You want a computer download capability of second-by-second samples from rides. You can identify situations where your pacing was off (started hard and faded, held back and had a strong finish), track training stress, and find parts of routes you're riding for other reasons (ex - commuting) which will let you ride uninterrupted intervals. You can apply feedback to your training plan - maybe you need more rest time, maybe you can sustain a higher ramp rate than what you started with. This needs to be compatible with your preferred training software (I like Golden Cheetah which is free and runs on Windows/linux/Mac).

You want enough data displayed at once. Current power if available, average power or heart rate over the interval, interval time, heart rate, and cadence. That's four or five fields. Add speed, distance, and lap distance if you find those motivating or interesting at the same time and the total is up to eight.

If you'll be riding in the evening or before dawn you want a back light which can be configured to stay on.

You want compatibility with ANT+ power meters. Using heart rate as an approximation is better than nothing, but it drifts upward so you don't work hard enough, lags behind so you spend your anaerobic energy reserve early, doesn't reflect effort on shorter intervals, doesn't lend itself as well to setting target intensities as power with a critical power plot, etc. Power meters are coming to the masses the same way that heart rate did decades ago.

The Garmins do all that, with the Edge 500 not costing appreciably more than computers that don't.

I got a Polar CS200CAD with heart rate and no download after I decided to be more methodical about riding. All training got logged manually, I only had averages, the back light wasn't good, hitting stop twice cleared the ride, the 5Khz wireless sensors glitched around power lines/street lights and threw off the averages, etc. I replaced it with a Garmin Edge 500 and added a used Powertap (I figured that if training with power didn't work for me I could resell it for what I paid. Worked great).

The Garmin does everything right apart from the software sometimes crashing when I hit the lap button and am using the Powertap; hopefully that goes away when I upgrade the firmware.

The Joule is similar, but more expensive and lacks GPS telling you where you've been.