I've owned the following relatively modern lights (I won't bore you with the older halogen lights I've had):

• Light & Motion Urban 900 -- I thought it was great while it lasted. But eventually a recessed manhole cover at 30 MPH exposed its Achilles heel: The flange molded into its body that mates with the handlebar mount snapped clean off, rendering it unmountable with anything less than duct tape. It was ruined. It lasted me less than one season. The other flaw is that its USB charge port cover falls off every time you open it (this is part of its design), and it is made of a plastic that grows weaker every time you open it until it eventually separates from its retention point forever. I wrote to L&M about this, and they acknowledged the flaw and sent me four more USB port covers (about a month before the mounting flange broke off). The daytime mode is similar to the oscillation of a sine wave; it oscillates between low and high, it doesn't strobe. I liked that it had side marker lights, though I don't think they're terribly effective.
• Light & Motion Taz 1200 -- This one actually is great, mostly. The mount has a metal screw that goes through it into the metal housing, so it's much stronger (I think). The mounting strap is designed to stay on the light always; you don't leave part of it on the handlebars when you remove the light. This light is pretty big, and while I do currently have it mounted on my commuter bike permanently (using a GoPro mount on my GPS out front bracket), a minimalist would consider it too much of a chunk. It is very bright, and has a nice configuration of three lights, one of which is behind a diffusing lens. The side markers are brighter than the Urban 900, and can be turned on and off when the front light is on. The main front light has low, medium, high, and daytime oscillating mode. The oscillating mode is not a strobe.
• Cygolite Metro 800: This light is much smaller than the Taz 1200 -- similar in size to the L&M Urban 900. Its brightness is perfectly adequate for city riding, even in the suburbs. It has a low, medium, and high mode. There are no side markers, which is fine with me because I have a separate side light. It has an off-bike flashlight mode that is useful when fixing a flat (it's lower power than any of the headlight modes, and lasts a good long time). There are two daytime modes; strobe, and strobe over solid. The strobe over solid mode keeps the headlight on in low mode, and overlays a slow strobe. I find this mode useful at dusk and dawn, when I need to be maximally visible. The strobe-only mode is best for a long day ride. The mount on the Cygolite is very good. It has an ample flange on the light's body that slides into a clamp that affixes to round handlebars. If you prefer you can obtain a GoPro mount for it and mount it under your GPS out front mount, too. I use this light on my road bike and ride it more evenings than not. This may not be quite as bright as my broken L&M Urban 900, but they do make brighter models, and it has a stronger mount than the Urban 900.

If I had to outfit both of my bikes all over again I'd probably get a couple of the brighter Cygolite Metro lights and be done with it.

I mentioned side lights above. I have one on each bike because I do a fair amount of my riding at night when the kids are asleep. On my commuter bike I have a Planet Bike Bottle Blinky, that mounts below the downtube bottle cage. On my road bike I have a Brightside Side Light.

I feel it's really important to be visible from the side. Some of the closer calls I've had have been when I proceed after a full stop at a 4-way stop sign only to have the cross traffic start up in front of me as if they haven't seen me. This is even with full headlight and tail lights. With side lights installed I haven't had this happen. They also seem to help with the person entering the roadway from a parking lot as I pass by on the road; they seem to see me better.

The Brightside is much brighter than the Bottle Blinky, and is rechargeable rather than using AAA batteries. Unfortunately it's harder to mount securely and usefully. One flaw it has is that its lens hoods only shade the top half of the lens, so you must mount the light with its bracket facing upward, or mount it behind you, out of your field of vision. If you don't, it's going to blind you at night. This means that mounting it on the front of the head tube, under the top tube, under the down tube, or under the stem is asking to be blinded by it at night. The best position I've found is near the top of the seat tube behind the tube, but the strap it comes with is a little too long, so it's slightly loose.

The Bottle Blinky isn't as bright, but is ideally located right below the downtube's bottle cage. This position may interfere with a pump, if your pump is mounted to the side of the downtube bottle cage.