Day trip to Cadiz from Sevilla

There's also train service, with travel times varying from just under 1-1/2 hours to a bit less than 2 hours. Most of the trips are on Media Distancia trains, which have a fixed fare of 13.30 euros each way. Those trains don't have assigned seating, so there's no advantage to buying the tickets in advance. The fastest of the trains are Alvias, with assigned seats and fares that vary with demand (and thus date of purchase). Late purchase of an Alvia ticket could cost around 30 euros each way. Personally, I don't think the minor difference in travel time is really worth the extra cost of an Alvia, but maybe someone else can tell us the Alvia carriages are nicer.

Most of the bus service between Seville's Prado de San Sebastian Station and Cadiz is operated by the company Comes. The buses are scheduled to take 1-3/4 hours, and tickets cost 17.45 euros each way.

Both the trains and the buses are easy enough; I'd feel no need to take a tour unless I felt I'd benefit significantly from the guide's information and was willing to accept the tour company's decision about how much time to spend at each stop. (That would probably be a deal-breaker for me, but I'm picky about that sort of thing.)

If you have awkward luggage, you might prefer a bus, because you can just roll your bag to the side of the bus and lift it into the storage area. It can be a bit awkward to get a suitcase onto some train carriages. But a Media Distancia train would be a bit cheaper than a bus. I'd consider the location of my hotel vis-a-vis the train station and the Prado de San Sebastian bus station (Seville has two bus stations). One might be easier for you to reach from your hotel.

You can find the train schedule here: https://www.renfe.com/es/en.

The Comes bus schedule is here: https://www.tgcomes.es/.

Use the Spanish spelling, "Sevilla".

I would take the train. In Cadiz, the main TI is just a few minutes' walk from the train station and another 2 minutes and you are smack dab in the center, can walk everywhere.

A benefit of the Media Distancia trains over the Alvia, besides the cost and flexibility, is that they serve Sevilla San Bernardo station which is better served by public transit vs. the long-distance Santa Justa station.

"Is it easy to take a bus or train to Cadiz from Sevilla or should we take a tour?"

Just from looking at Google Maps and seeing the route and what train to take and how long it takes to get there, it seems pretty easy. Personally, I would avoid a tour. I don't like being herded around. When I'm on a tour, I seem to spend half my time and effort following the person in front of me and trying to hear what the tour guide is saying.

We were in Sevilla last year, and I regret not taking a day trip to Cadiz. That seems like such a fantastic city.