The difference in commissioning an open bar vs. a cash bar comes down to hospitality, etiquette and manners. Your guests are just that: guests and expect to be treated as such. It's like you offering to host a few of your friends at your home but ask them to bring their own beverages.
In the wedding world, it's proper manners to have an open bar because ultimately your guests are there for you. If you think about it, of all the people you two know combined, you invited the select few to celebrate with you and, in theory, you want to extend the best possible hospitality.
LIMITED ON FUNDS FOR YOUR WEDDING BAR SERVICE?
You could limit your wedding bar service to beer and wine plus 2 signature cocktails, a his and hers, so that you don’t have to fully stock an entire bar.
I try to steer my clients clear of this option but is feasible if you really need to cut some corners. Instead of hosting an open bar for the entire evening, you can host it partially. For example instead of hosting the bar for 6 - 8 hours, I suggest that you host it for about 4 - 6 hours. If planned out correctly, this should lead into the time for toasts and a little bit into the dancing segment of your wedding day. At this point the elderly will have left, if children were allowed then parents may have taken them home for bedtime and hopefully your guests have been enjoying your wedding bar service to this point to keep the party going.
IN MY OPINION
In addition to doing everything in my power to serve and satisfy my bride and groom, I do my best to appease your guests. Weddings should be an experience for everyone because you are planning so much and paying a considerable amount of money, the last thing you want is for your guests to feel uncomfortable. This is a time where friends and family get together and hospitality plays a BIG role in that. I would HIGHLY recommend hosting the entire bar for the entire event.
Make sure your Mixologist has a good reputation, is a professional and has great reviews. You’ve heard the horror stories where the bar didn't have enough alcohol and ran out during cocktail hour (that happened at a wedding this weekend actually where I wasn't involved with the planning). A professional will know what they need to bring and will ask you the type of guests you are inviting so they can recommend the right amount of alcohol based on your demographic. You also want someone who is able to read people in the case where they need to cut a guest off or help identify a potential issue to prevent it from getting worse on your wedding day.
For more tips about bar services, visit Mint Bartending