Yes, mineral sunscreens are a better choice for you if:
Your skin is extremely sensitive.
Your skin is somewhat sensitive and you shop for a sunscreen in the US (Avobenzone, the best broad spectrum organic filter fully approved by the FDA, can be an irritant).
You tend to get your sunscreen into your eyes (organic filters can sting the eyes).
You are choosing a sunscreen for a baby or young child (it's best to treat children's skin as extremely sensitive by default).
Sunscreens that contain only the inorganic filters (zinc oxide and titanium dioxide) are sometimes called "mineral", or "physical" ("inorganic" or "nonorganic" in chemistry denotes a compound that does not contain carbon). The other type of sunscreens labeled "chemical" contain organic UV filters (as in compounds with an atom of carbon).
A huge advantage of mineral sunscreens is that they are very unlikely to cause skin irritation, don't sting the eyes (or skin), and are stable (as in they don't lose their effectiveness when exposed to the sun).
Unfortunately, they have disadvantages too. Their cosmetic elegance (or lack of it) is a huge one. Mineral filters generally require quite a thick product texture to function properly, and more often than not, they leave a white to grey, chalky finish on the skin. This is often a no-go for darker skin tones. In the recent years, formulators have been able to achieve way more elegant formulations using very finely milled and coated zinc oxide particles (microfine and nano particles).
The other challenge with the non-organic filters is that they are not the strongest ones. 10% Zinc Oxide (nano), for example, on average, provides an SPF of about 5 (without additional sunscreen boosters). 10% of Titanium Dioxide provides an SPF of about 20, but 10% of titanium dioxide looks very, very white and not appealing. In addition, Titanium Dioxide cannot offer a sufficient protection from the UVA rays (the long ones, UVA I).
Overall, formulating a sunscreen with mineral filters only that is able to provide a sufficiently high protection from both UVB and UVA rays while being cosmetically acceptable for daily use is very difficult. Hence such products are a rare find, and typically provide an SPF not higher than 30.
How about the famous physical sunscreens with SPF 50 - e.g. Skinceutical's Physical Fusion UV Defense ? Well, sunscreens like this tend to be not entirely "physical" or "mineral". For example, the Skinceutical's product, in addition to Zinc Oxide and Titanium Dioxide, contains an ingredient Butyloctyl salicylate. It is an organic UV filter and is a relative of popular sunscreen filters Homosalate and Octisalate. Butyloctyl salicylate can absorb UV radiation but is not approved for use as a sunscreen filter in cosmetics on its own. It can however help boost the sun protection in a product, allowing it to get a higher SPF rating. There is absolutely nothing wrong with it, apart from potentially misleading marketing that positions these products as "mineral" sunscreens. It also means that products like this do not have the safety profile of a mineral only product (as in they have a higher irritation risk).
How about the organic, or "chemical" sunscreens? While there are only 2 non-organic sun filters, there are dozens of organic ones, which makes it difficult to speak about them as one group. Some of the early organic sunscreen filters (for example, Oxybenzone, Sulisobenzone, PABA) are frequent irritants, while others (for example, Tinosorb M and S, Homosolate) seem to have a low irritation risk. Some of the "chemical" filters are unstable (as in lose their effectiveness quickly when exposed to sun, for example, Avobenzone), while others are very stable (for example, most "new generation" filters like Mexoryls and Tinosorbs). The best UVA protectors are in the organic sunscreen group.
Overall, the rule of thumb is that the "new generation" filters are better an all fronts (broad spectrum protection, efficiency, and stability) compared to the early organic filters and, if formulated well, can rival the safety of mineral products.
Here is a catch though: unfortunately, most of the "new generation" organic sun filters are not available in the US because they are not approved by the FDA (while they have been safely used for decades in Europe and Asia).
The bottom line: mineral sunscreens used to be a better choice because of their lower irritation risk and stability. They remain the best choice for very sensitive skin, for somewhat sensitive skin if you live in the US, and for application in the eye area. However, in all other cases, the new generation "chemical" sunscreen filters provide a more reliable broad spectrum protection .
Photo by Luis Graterol