Not really. They both have their pros and cons, so neither is really better than the other. The consolizer runs games very slightly faster, on the other hand GBI keeps games running at original speed but has to employ one of several methods to make the framerate match up better with the framerate of the video output from the console (which differ slightly), which of these is better is purely a matter of personal taste, but at least GBI gives you more options for how the game is displayed on screen to suit the tastes of more people.
Also, with the Consolizer you have to sacrifice a GBA, since it won't be usable as a handheld anymore. It also removes certain other features like the ability to use batteries, which may or may not matter to you. It matters less if you get the version of the consolizer that has a controller port, but might be annoying if you get the other version that keeps the GBA shell and allows you to use it as a plug & play console with the original controls intact.
More info on the pros and cons can be found in this video:

I'd say if you already have a GB Player there's not much point in switching. Neither solution is perfect, but both of them work well and the vast majority of people would be happy with either.

 

GBA consolizer only supports 720p, which is crying shame because many tv's, mine included, suck at scaling 720p. However, if you go with the cheapest option it "only" costs $140.

GBI, on the other hand, has an option to display 360p which can be scaled to 1080p with an OSSC and looks absolutely stunning! This costs a ton of money, though. You need:

1. GameCube + Game Boy Player ~$60
2. GameCube component cables or GCHD ~$160
3. Way to run Homebrew ~$6
4.OSSC ~$180

You're looking at more than $400! This really is the ultimate way to do it, but it's gonna cost you. It's really dissapointing that the consolizer only does 720p because if it did 1080p there would be no contest.

 

That's why you need the component cables or the GCHD Mk II. In this case it might be cheaper to go with the official component cables. GCHD costs $150 and decent Wii component cables cost ~$25.

This Friday that just passed, I managed to get the official component cables for $150 on eBay.

Insurrection is selling GameCube component cables for $90, but unfortunately they don't support 360p. It's a real missed opportunity.

 

Wii component cables won't do you much good on a GC though.

 

Now that you mention it, i do remember hearing about that. Too bad it's so expensive.

 

Yeah, plus 720p doesn't integer scale to 1080p, so there is inevitably some additional sharpness loss from having that extra step. Something no one who pays this much to get the best quality possible should be okay with.
It does however integer scale to 4K. One of the nice things about 4K TVs.