That's a huge debate
In my opinion, between the 2 design options (first stage vs boosted stage), there's no clearly one that's better than the other on every point of view, even if I have a preference for the boosted design. That's an optimization problem in which you tend to gain on one side what you lose on the other side.
For the "first stage" design, the advantage is that when the first stage runs out of fuel, your second stage is full, which gives you the maximum delta-V available at that point. On the other hand, your first stage will do the job alone and will have to be more powerful.
For the "boosted" design, the advantage is that you have more thrust available in the beginning because the main core adds its power to those of the boosters (for a similar number of engines). However, after booster separation, the second stage is partially empty, meaning you have some dead weight to propell now.
As Horus said, there is an option that consists in transferring the fuel from the boosters to the main core to maintain it full until separation. That way, you cumulate the advantages of both designs. But as you can only transfer 1 ton of fuel per second, that method also has its own limits, especially for big launchers.
Overall I tend to prefer the boosted design, as it allows smoother transitions: as you know, TWR is important in the first part of the flight. But if we often look at the TWR at start, it must be remembered that because fuel is consumed, the TWR increases inflight. And this is even more true if you remember that gravity decreases with altitude (at Karman line, gravity is already lower by 20%). Problem, as you gain speed, you actually need less and less TWR, so it doesn't go naturally in the good direction
The booster design allows to adjust more smoothly the TWR ratio inflight: the boosters give you the kick you need in the beginning of the flight, your TWR increases, and then you drop the boosters: it means less dead weight from now on, and your TWR drops back to a more appropriate value. It even happened that I made a launcher with two levels of boosters to use this twice in a flight. Even if the main reason for this was because I hadn't enough thrust with one level of boosters. That's a cheap option to avoid redesigning a launcher
With a purely staged design, you can't tweak your TWR as accurately: when you perform your first stage separation, your TWR drops from "very high" to "very low", before slowly increasing again. Note that you can accomodate from that too: the last seconds of high TWR allow to put the launcher on a long ascending trajectory, it keeps climbing while the second stage starts burning, and by the time it reaches the top of its trajectory, its TWR became acceptable again. That's why I said there's no definitive answer to that debate.
Overall, I like the booster design though. Here is an example:
My favorite toy!
Here are its specifications:
Payload: 1350 tons
Main core: 1268.8 tons, 1200 tons of thrust, 290s Isp, 1053 tons of fuel, fuel consumption: 4.138 tons/s, burn time: 254.5s
Booster: 1180.3 tons, 2400 tons of thrust, 240s Isp, 996.75 tons of fuel, fuel consumption: 10.0 tons/s, burn time: 99.7s
Overall, the TWR at start is 1.2. With the same number of engine, the boosters alone could not lift that rocket if they were assembled in a single first stage.
The contribution of the main core is crucial here. However, on booster separation, I've already spent 40% of fuel from the main core, which represents 46.8 tons of dead weight. Sounds a lot in absolute, but that's a super launcher, it's not that much. That's still nearly 47 tons of dead weight I'll have to satellize, but that's the price to pay for the additional TWR at start, and that's quite a fair one. The only alternative would make me add more engines. In the end, if the number of engines or global thrust are the criteria for efficiency, the booster design is arguably the best approach here.
Also, one last word, one thing to be aware is that this debate is specific to SFS, it's quite different in real life.
In real life boosters (SRB) are relatively cheap to design (no turbopump, no complex plumbering, no cryogenic fuel...), so it's a good option to reduce costs. Apart from crewed module liquid fuel engines are the most expensive part of a launcher. That's also a good option to adjust the payload capacity of a launcher. Some rocket families rely on that: Ariane 6 will come in 2 versions: with 2 or 4 boosters. Ariane 4 could be used with 0, 2 or 4 boosters, and there was 2 kinds of boosters: solid and liquid (liquid was more performant but more expensive). The Atlas V can use 0 to 5 boosters too.
Some other rocket families use a pair of first stages to make a heavy version: the Delta 4 heavy or the Falcon Heavy. The Ariane 6 booster is also a Vega's first stage.
Overall, the logic behind the booster design in real life is rather in terms of versatility and cost reduction, so those are different considerations from SFS.