Alot depends on how old yours is, but Nothing beats a phone for ease of use.  The audio quality on my phone mics works just fine.  For an all in one package its perfect.  You can record audio only if you want.  You can make a video and even do most video editing work right on the phone and publish to youtube or other social media. 

I think the only reason to go with some kind of mic and computer setup with higher end editing software and gear is if you want to experiment with THAT in itself.   Using something like audacity or protools or in my case presonus allows you to multitrack different instruments, real or virtual.  It opens up possiblities music wise, whether thats good or bad. 🙂  It can have some learning bonuses.  But it also can eat up alot of valuable practice time and money.  I enjoy multitracking for fiddle stuff, and have learned tunes just by recording takes.  Ive learned them without too.  But, I really enjoy doing that kind of stuff and is an additional hobby along with playing fiddle.

I dont think your missing out on anything by using a phone or tablet, unless youre interested in making multitracked recordings.  

Just for something to look at...rode makes some camera microphones that may be a step up.  If you have a mirrorless or dslr type camera with an external mic jack, you can use something like what rode makes and have stereo mic audio.

Zoom makes some great music oriented cameras that focus on better audio, but the video isnt much better than most phones. 

Those may be something to consider if youre just wanting to try something different video wise.