I'll be honest. I took the bracket off my bike for race season and haven't had this pump on my bike for nearly a year, but it's a product that I really do like. Is it as quick and easy as a CO2 cartridge? No, but it is far more reliable. I've seen CO2 inflators fail at least a dozen times for a variety of reasons. For some reason, it seems to happen even more often when it's cold outside. What happens after your first CO2 fails? If you are lucky, somebody else on the ride has one. Otherwise, you're calling for a ride. What if you pinch a tube upon installation, or get the dreaded double flat on a ride? A patch kit and mini pump will get you home.
There are a ton of different mini pumps on the market. If you have a decent size saddle bag, you might be able to buy a pump small enough to fit inside it. This is a great option, because it is always with you and stays out of sight, and out of the conditions (rain, salt, sand, grime, etc.). There's a downside. The smaller the pump, the more strokes it will take to inflate your tire, and the longer it will take too.
If you get a bigger pump that doesn't have a frame bracket, you'll have something that pumps more efficiently. The downside is that you'll have to remember to pack it every single ride.
The Lezyne Pressure Drive is a pretty decent size. It's only about 100g, so it's not going to weigh your bike down much. It comes with a bracket that conveniently connects the pump right behind your bottle cage. With a bottle in the cage, the pump is more or less out of the wind, except for maybe a strong crosswind from your right side, so it isn't causing much of an aero penalty either.
The thing that won me over with the lezyne was that it comes with a hose that threads on to your valve. It works on both schrader and presta valves. You don't have to hold the end of the pump onto the valve with one hand and pump with the other. You can pump with both hands. The hose seals nicely on the valve, so air isn't leaking out as you pump it in. The Pressure Drive model easily inflates the tire to a high enough PSI to get you home. They claim 120psi. Maybe, but it will be tough. Getting it up to about 90psi is a piece of cake, and it doesn't take very long.
On training rides, you end up becoming everyone's favorite rider if you have a nice pump. Best case, it saves them a couple dollars on a one-time-use CO2 cartridge. Worst case, it gets them home after their CO2 fails.
Lezyne has lots of different models. If it's for your road bike, definitely get a High Pressure model. The low pressure ones for mountain bikes have a higher volume of air so they pump quicker, but they will be difficult to get up to high pressures. They have some high pressure models that have a built in gauge. Cool feature, but totally unnecessary. They also have carbon ones, but to me it's silly to spend double the price just to save a few grams on a carbon pump.
Other brands make similar pumps too. Bontrager has one that looks almost exactly like the lezyne. It mounts the exact same way. It has a steel braided hose instead of rubber. That's pretty cool, I guess. I think retail was $5 more. I haven't tried it out, but judging by the size and look, it's probably a good pump. In theory, these pumps should last a long time, since you rarely have to use them. I've already had this Lezyne for years, and I'm hoping it will be the last frame pump/mini pump I ever have to buy.