led viewing angle q's

Welcome to the boards.

"Bright" is not a sufficiently precise term here.

Assuming all ratings are accurate and describe the average luminous intensity of the beam across the full cross-section (not a particularly good assumption in practice, actually): then there is more luminous flux emitted from the device with the 45 degree beam.

OK, now, what did I just say, without resorting to jargon?

Think about a source of photons. The number of visible light photons that leave it per second is described as the luminous flux, measured in lumens. If you take the same luminous flux and focus the beam into a narrower pattern (beam width), you will produce a higher luminous intensity, measured in candelas.

For example, think about a Mag-Lite flashlight with a focusable beam. The lamp in it is sending the same amount of photons out, but you can spread them out over a wider beam angle. If you have a light meter anywhere in that beam, the illuminance that you will measure (in units of lux) will also decrease as you spread the beam out. When you measure illuminance you are getting a measure of how many photons land on a unit of area. This measurement, unlike the other two, is dependent on distance from the source. (It inversely varies as the square of the distance, to be specific.)

Out of all these units, the one that corresponds best to "bright" (which is a perception, not a measurement) is illuminance.

The reason bright is a perception: human vision is adaptive. If your pupils open up because you've been sitting in the dark, I can use a 5mm LED to practically blind you. But if I took that same LED in the daytime and shined it right at your eye, you would barely notice. Your vision would have adapted to the higher light levels.

So, recapping--the question you asked doesn't exactly have an answer. But more photons are emitted by the 45 degree device, subject to the assumptions noted above.

If you describe your application in more detail, it may be possible to give you better advice.

1 watt = <some number of> photons/second
1 lumen = <some number of> photons/second, weighted to the response of human vision
1 candela = 1 lumen/steradian, where a steradian is a measure of solid angle
1 lux = 1 lumen/square meter.