Nearly every article about which booking system to choose is written by a company that sells one, and nearly every one puts its own product first. I am writing this one as the maker of one of them, Rezervos, so I will not rank anything. I will lay out how to decide, and where others are better.
You might not need one
If you cut alone, your clients are regulars and they book the next appointment from the chair, a paper diary or the calendar on your phone is enough. Booking software starts to make sense when appointments are split between several people, when the phone interrupts you mid-cut, or when clients message about a slot at eleven at night and expect an answer by morning.
First decide whether you want new clients
This is the most important decision, and most comparisons skip it. The systems fall into two groups.
Marketplaces such as Notino Partner or Fresha show you to people looking for a salon nearby in their app. That is a real advantage, especially when you are starting out. The price is that a client finds you next to five other salons on the same street, and the next time they open the app, it offers them all of them again.
Systems without a marketplace will not bring you clients. Booking happens on your website or through your link, and the client sees only you. They suit you when you already have a clientele and mainly need your appointments in order.
What decides it is whether you are short of clients right now, or short of time.
How you pay
Notino Partner says it is completely free for salons; you pay by being part of their marketplace. Reservio has a free plan with paid upgrades. Fresha charges a monthly fee per team member, plus card-payment fees. Rezervos has a permanent free plan and paid plans with a flat fee per venue.
What to look at: how much you will pay once there are more of you. A per-person fee is cheap with one chair and not with four. And read what the free version leaves out. Rezervos’s free plan, for example, sends no reminders, and for a salon reminders are the most valuable part.
What even the cheapest one must do
Let clients choose a specific barber or stylist. People come for a person, and a system that assigns them to "whoever is free" puts them off after the first try.
Handle services of different lengths. A cut, a cut with a beard trim and a colour are not the same length, and setting them all to one slot gives you either gaps or a running delay.
Send a reminder the day before with a cancel link. A forgotten appointment is the most common reason someone does not turn up, and cancelling with one click is easier for the client than calling.
Give you a link you can put in your Instagram profile. That is where clients make up their minds, so let them book there too.
Export your clients. If you ever move elsewhere, the contact list is yours and you should be able to download it.
Walk-ins
People search surprisingly often for a "hairdresser without an appointment" or a "walk-in barber" in their town. If you take walk-ins, a booking system does not have to change that. Keep part of the day free in it: online bookings until three, say, and the afternoon for whoever walks in. A system that will not let you block time for yourself makes you choose one or the other.
Where others beat Rezervos
Rezervos is a business website with booking inside it, for a flat fee, invoiced in the Czech Republic. It will not bring you clients, because it has no marketplace of its own. If new clients are what you need, Notino Partner or Reservio will do more for you. Reservio, Bookio and Altegio all have a more developed client record for beauty businesses, and Bookio has a point-of-sale system, which Rezervos does not have at all.
I go through it in detail in the comparisons with Reservio, Bookio and Altegio.
How to try without risk
Pick the two systems that make sense to you after the sections above and take real bookings in each for a week. Then go through booking on your own phone, as a client would. That will decide more than any feature list, because a client who does not like the booking page simply calls.
If you want Rezervos to be one of the two, the hair salon demo opens without signing up.