You have cantilever brakes. Centerpull brakes are similar but do not have cantilever posts installed on the frame or fork. That said, some people call the ones you have centerpull cantilever.
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Try the canti brakes first before you think about replacement. I have canti brakes on my rando bike, my Thorn Sherpa (medium touring bike), and my errand bike.
My recent experiemce endorses that suggestion. I had good cantilever brakes in good shape on the Trek I replaced last year with my Thorn Mercury.
The Mercury has a V-brake up front and a mechanical disk brake at the rear.
One thing I did not notice after the switch was greatly superior braking.
I am not convinced the V-brake was designed to improve braking power, even though it has the potential to do so through an increase in leverage.
I think it was designed mainly to save weight. When introduced on mountain bikes, V-brakes came with much smaller and shorter brake levers. The increased mechanical advantage of he V-brake caliper allowed the design to accept reduced mechanical advantage at the lever.
The levers on my Trek (straight 'bars) look like motorcycle brake levers by comparison. But they allow me to apply lots of force.
Having said that, if you're switching to straight 'bars and therefore need new levers anyway, you'll likely find V-brake lever and caliper combos easy to come by and they should fit the same frameposts as the cantilever units.
Its a long while since I've used drop handlebars but FWIW I used them exclusively in my 20s and I do think they offer a better range of hand positions than straight bars, even with the Ergon grips and bar ends now recommended by Thorn. You can ride up on the flats, or with your hands in several places around the initial curves, or forward on the brake hoods, or when climbing, facing a headwind or maximising descent speed either forward on the drops or right down on the drops.
No doubt though, access to brakes and gears is inferior. I never found the brake side of that a problem for road use. But it would annoy me a lot these days on gravel descents, where I would be forced onto the drops if I wanted swift access to maximum braking power.