Cruise Ship Excursions vs Do Your Own Thing

In a manner of semantics, you have provided three options.
1. Opt In with the cruise line's tour.
2. Locate and hire a local guide.
3. Go it on your own, which would require some research on your part.

There are some benefits to each option.
The cruise line's offering may well be the highest price but when (or if) your ship arrives late,
their offering is either guaranteed or refunded.
The local guided tour, while probably a better value isn't waiting for your late arrival (if that is a factor)
so you are out.
If you elect to go it alone, no pre-paid tour is at issue. The "value" of your "go it on your own" will
depend on the depth your research.
I should mention, I have taken exactly one ocean cruise so my remarks do not represent those of a reliable traveler.

And just to add more 'it depends' to the above- it depends on the port, what there is to do there, what you want to do, and how far from the port you need to go. Some ports, such as the larger ones in the Caribbean, have a great many options, with drivers and guides just waiting at the gates. Others, docking in smaller ports may have few options available , or may require travel some distance away from the port. In the latter case, taking the more expensive cruise excursion might be the prudent thing, since the ship will wait if it's own excursion is late returning. It's wise to book a private or independent small group tour in advance. And it's practically mandatory to do your research well in advance if opting to DIY.

All else being equal, we rarely take a ship excursion if there are other, reasonable choices available. Beach/shopping/casual wandering are almost always DIY. But for real sightseeing and visits to historic sites we prefer to book with an independent tour outfit.

We've only done two cruises and they were with Viking. We only did a few tours that were not included with the cruise that cost extra. If the ship docks near or at city center, I'm likely to do some research and do my own touring. With Viking, the extra tours seemed quite expensive, however, with the ship's own tours, there is no risk of them leaving without you.

Using a cruiseship's tours would be a last resort for me. I base that on the ridiculous pruce they charge and also a desire not to be stuck on a bus tour with 50 others. We haven't done an ocean cruise in many years, but in the 5 cruises we have taken, we used the ship's option once, booked outside tours once and did it on our own the remainder of the ports.

Agreeing with all of the above. We've done many Mediterranean cruises over the years and taken just one ship excursion: to Tunis. I just couldn't figure out how to get from the ship to the city to see what we wanted to see without the ship's offer. Otherwise, I've done one private excursion to Ephesus. That was very good value given the distance from the ship to the site and the services of the guide. All of the other port stops were easy enough to navigate with enough pre-planning. Very often, the ship either docks (or tenders) close enough to public transport that we can walk or we take a cab to bus/train/subway and go from there. You do need a sense of adventure and the ability to switch gears if part of your plan goes sideways. You don't want to left behind.
happy planning!

Others will offer other opinions, and that is ok. But our advice, based on having taken well over 20 cruises is:

It is ok to do it on your own (or use a local guide) if you will not be going very far afield and can get back to the dock on your own. However, if you going any distance from the area of the dock, then take the tour offered by the cruise line.

Yes, the cruise line tours are expensive, but not as expensive as getting yourself to the next port if you literally miss the boat. If you are not on a cruise line tour and do not get back in time, the ship will leave you. Period. We've seen (on a number of occasions) people running along the dock as the ship departed.

What could make you late for the departure? Traffic jams, auto accidents, demonstrations, mechanical breakdowns, and unexpected weather problems. We've experienced all of them on excursions that took us far away from the port, and the ship always waited.

Don't mean to rain on your parade, just offering food for thought.

This would be an easier question to answer if we knew what cruise company you are with. For example, we did an included tour to Ephesus that was fantastic on our Viking cruise. Couldn’t have asked for more.

I agree with TC. We've taken a number of cruises, and we either choose the cruise line excursion, or go into town and wander around on our own. The primary question is your risk tolerance. For us, after spending lots of money to get someplace, spending a few more dollars to know we'll get back to the ship on time, and also not be fleeced by someone I hire on the pier, is most important.