That is the $64,000 question, adjusted for inflation to, say, a round million today!
Such a decision comes down to personal preferences and your personality, time frame, finances, your sense of independence, what you want to see and do, where and how far you want to bike and, perhaps most important, the flexibility to do whatever, whenever.
Do you enjoy meeting new people and spending a good part of the day and night with them as a group? Or are you more comfortable with one or two others, such as those you already know.
How much time do you have or want to take? Is your schedule open-ended or limited? Many guided trips cater to those with limited time, leaning toward one- and two-weeks' duration.
Is money an important factor, since a guided tour will be significantly more expensive (depending on various factors) than a self-planned and -guided trip? Do you want to camp or stay in B&Bs, guesthouses, hostels or hotels? Do you want to cook your own meals, have them catered by a tour operator or eat in pubs and restaurants of your choosing?
Would you rather be on your own or have the security and convenience of biking with a group of ten to twenty others for example? How skilled are you doing basic bike repair and maintenance tasks? Do you want to carry all your stuff or have someone else deliver it to your hotel?
How do you feel about following a proscribed route and daily schedule? Or is picking and choosing your own daily routes - and overnight spots - more to your liking? Organized tours often offer short biking days (30 miles or so) so as to allow more time to explore various towns and attractions. On your own, you bike as far as you wish and are able.
What cities, towns, places, sites and the like do you want to visit and see? Do you want to sleep in a different town and facility each night or base yourself out of a few towns for more localized day rides?
Lots of food for thought, with pros and cons for each style of travel.
I've led and gone on many short and long organized trips with AYH back in the day when outdoor travel was its mainstay. Bicycle touring is a very social activity and was the heart of small-group AYH trips.
Mostly though I've planned my own trips all over Europe and other places. If you have a liking for logistics and planning, are good with detail, prefer flexibility and serendipity over structure and friends over strangers, then independent travel is the way to go.
Either way, I'd say you can't go wrong.