Probably teaching my grandpa/ma to suck eggs with this reply but I figured other people may read your topic who don't know anything about mi-fi or what's available
A mi-fi unit works on exactly the same principle as mobile phone data, ie connecting to the internet via a sim card. The main difference was that a mi-fi device connects itself to the internet and then puts out a wi-fi signal, so you can connect a phone, laptop, tablet, etc, all at once, usually up to 5 devices. These days though, most phones will allow you to set them up as a 'hotspot', so that you can share the connection in the same way. Personally, I've found that my mi-fi unit usually gives me a better internet connection than my phone but it's possible that could be about the mobile provider rather than the device I guess. You can buy mi-fi devices that have an aerial socket... stick the aerial outside the skylight for an even better signal. When all's said and done, it's still a sim connection but if your phone is 3G and a mi-fi is 4G, then you'll gain speed using the mi-fi's wireless signal.
The big drawback with using your phone as a wi-fi hotspot is that you're stuck with your own phone sim and whatever data allowance you get through your provider. If you can't get a signal somewhere on your phone, then that's it, no signal. With a mi-fi unit, provided you have an unlocked one, you can switch to a spare PAYG data sim from any other mobile company... and could even buy a local one abroad if that looked like a better bargain. Personally, I don't think it's worth getting a data sim on contract, a) because you're stuck with one company again and b) because you can pay around £2 per GB for PAYG data and that's far cheaper than with most contract data sims, plus you don't have to lose any data if you don't use it within a month. For example, Trio sims from 3 are really good value and have good coverage in the UK and Europe. The 12GB one is valid for up to a year (depending how quickly you use the 12GB) and the 24GB one is valid for up to 2 years. They're currently £28 and £45 respectively... see links below.